Same-Point Orbit-Stabilizer Counts, Fibers and Left-Coset Certificates

1. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1}, total action_table=[[0, 1], [1, 0]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

2. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

3. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

4. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

5. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

6. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 0, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

7. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

8. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

9. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 0, 5], [2, 3, 4, 0, 1, 5], [3, 4, 0, 1, 2, 5], [4, 0, 1, 2, 3, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

10. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 0, 6], [2, 3, 4, 5, 0, 1, 6], [3, 4, 5, 0, 1, 2, 6], [4, 5, 0, 1, 2, 3, 6], [5, 0, 1, 2, 3, 4, 6]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

11. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

12. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

13. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 0, 4, 5], [2, 3, 0, 1, 4, 5], [3, 0, 1, 2, 4, 5]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

14. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 0, 5, 6], [2, 3, 4, 0, 1, 5, 6], [3, 4, 0, 1, 2, 5, 6], [4, 0, 1, 2, 3, 5, 6]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

15. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 0, 6, 7], [2, 3, 4, 5, 0, 1, 6, 7], [3, 4, 5, 0, 1, 2, 6, 7], [4, 5, 0, 1, 2, 3, 6, 7], [5, 0, 1, 2, 3, 4, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

16. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

17. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

18. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 0, 4, 5, 6], [2, 3, 0, 1, 4, 5, 6], [3, 0, 1, 2, 4, 5, 6]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

19. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 0, 5, 6, 7], [2, 3, 4, 0, 1, 5, 6, 7], [3, 4, 0, 1, 2, 5, 6, 7], [4, 0, 1, 2, 3, 5, 6, 7]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

20. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 0, 6, 7, 8], [2, 3, 4, 5, 0, 1, 6, 7, 8], [3, 4, 5, 0, 1, 2, 6, 7, 8], [4, 5, 0, 1, 2, 3, 6, 7, 8], [5, 0, 1, 2, 3, 4, 6, 7, 8]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

21. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

22. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

23. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 0, 4, 5, 6, 7], [2, 3, 0, 1, 4, 5, 6, 7], [3, 0, 1, 2, 4, 5, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

24. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 0, 5, 6, 7, 8], [2, 3, 4, 0, 1, 5, 6, 7, 8], [3, 4, 0, 1, 2, 5, 6, 7, 8], [4, 0, 1, 2, 3, 5, 6, 7, 8]] and specified point=5. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

25. The Same Point Binds Both Factors in Orbit-Stabilizer Counting

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(10)={0,…,9}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 0, 6, 7, 8, 9], [2, 3, 4, 5, 0, 1, 6, 7, 8, 9], [3, 4, 5, 0, 1, 2, 6, 7, 8, 9], [4, 5, 0, 1, 2, 3, 6, 7, 8, 9], [5, 0, 1, 2, 3, 4, 6, 7, 8, 9]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-counting-identity · candidate

26. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1}, total action_table=[[0, 1], [1, 0]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

27. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

28. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

29. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

30. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

31. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 0, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

32. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

33. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

34. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 0, 5], [2, 3, 4, 0, 1, 5], [3, 4, 0, 1, 2, 5], [4, 0, 1, 2, 3, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

35. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 0, 6], [2, 3, 4, 5, 0, 1, 6], [3, 4, 5, 0, 1, 2, 6], [4, 5, 0, 1, 2, 3, 6], [5, 0, 1, 2, 3, 4, 6]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

36. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

37. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

38. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 0, 4, 5], [2, 3, 0, 1, 4, 5], [3, 0, 1, 2, 4, 5]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

39. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 0, 5, 6], [2, 3, 4, 0, 1, 5, 6], [3, 4, 0, 1, 2, 5, 6], [4, 0, 1, 2, 3, 5, 6]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

40. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 0, 6, 7], [2, 3, 4, 5, 0, 1, 6, 7], [3, 4, 5, 0, 1, 2, 6, 7], [4, 5, 0, 1, 2, 3, 6, 7], [5, 0, 1, 2, 3, 4, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

41. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

42. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

43. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 0, 4, 5, 6], [2, 3, 0, 1, 4, 5, 6], [3, 0, 1, 2, 4, 5, 6]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

44. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 0, 5, 6, 7], [2, 3, 4, 0, 1, 5, 6, 7], [3, 4, 0, 1, 2, 5, 6, 7], [4, 0, 1, 2, 3, 5, 6, 7]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

45. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 0, 6, 7, 8], [2, 3, 4, 5, 0, 1, 6, 7, 8], [3, 4, 5, 0, 1, 2, 6, 7, 8], [4, 5, 0, 1, 2, 3, 6, 7, 8], [5, 0, 1, 2, 3, 4, 6, 7, 8]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

46. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

47. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

48. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 0, 4, 5, 6, 7], [2, 3, 0, 1, 4, 5, 6, 7], [3, 0, 1, 2, 4, 5, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

49. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 0, 5, 6, 7, 8], [2, 3, 4, 0, 1, 5, 6, 7, 8], [3, 4, 0, 1, 2, 5, 6, 7, 8], [4, 0, 1, 2, 3, 5, 6, 7, 8]] and specified point=5. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

50. All Action-Map Fibers Have the Same Stabilizer Cardinality

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(10)={0,…,9}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 0, 6, 7, 8, 9], [2, 3, 4, 5, 0, 1, 6, 7, 8, 9], [3, 4, 5, 0, 1, 2, 6, 7, 8, 9], [4, 5, 0, 1, 2, 3, 6, 7, 8, 9], [5, 0, 1, 2, 3, 4, 6, 7, 8, 9]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Give (action_map, fibers, equal_fiber_sizes, orbit, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-action-fibers · candidate

51. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1}, total action_table=[[0, 1], [1, 0]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

52. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=0. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

53. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

54. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=2. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

55. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=3. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

56. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 0, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=2. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

57. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=0. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

58. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=2. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

59. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 0, 5], [2, 3, 4, 0, 1, 5], [3, 4, 0, 1, 2, 5], [4, 0, 1, 2, 3, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

60. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 0, 6], [2, 3, 4, 5, 0, 1, 6], [3, 4, 5, 0, 1, 2, 6], [4, 5, 0, 1, 2, 3, 6], [5, 0, 1, 2, 3, 4, 6]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=0. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

61. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=2. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

62. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

63. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 0, 4, 5], [2, 3, 0, 1, 4, 5], [3, 0, 1, 2, 4, 5]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

64. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 0, 5, 6], [2, 3, 4, 0, 1, 5, 6], [3, 4, 0, 1, 2, 5, 6], [4, 0, 1, 2, 3, 5, 6]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=6. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

65. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 0, 6, 7], [2, 3, 4, 5, 0, 1, 6, 7], [3, 4, 5, 0, 1, 2, 6, 7], [4, 5, 0, 1, 2, 3, 6, 7], [5, 0, 1, 2, 3, 4, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=6. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

66. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=0. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

67. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=4. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

68. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 0, 4, 5, 6], [2, 3, 0, 1, 4, 5, 6], [3, 0, 1, 2, 4, 5, 6]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

69. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 0, 5, 6, 7], [2, 3, 4, 0, 1, 5, 6, 7], [3, 4, 0, 1, 2, 5, 6, 7], [4, 0, 1, 2, 3, 5, 6, 7]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

70. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 0, 6, 7, 8], [2, 3, 4, 5, 0, 1, 6, 7, 8], [3, 4, 5, 0, 1, 2, 6, 7, 8], [4, 5, 0, 1, 2, 3, 6, 7, 8], [5, 0, 1, 2, 3, 4, 6, 7, 8]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=3. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

71. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=2. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

72. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=1. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

73. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 0, 4, 5, 6, 7], [2, 3, 0, 1, 4, 5, 6, 7], [3, 0, 1, 2, 4, 5, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=6. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

74. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 0, 5, 6, 7, 8], [2, 3, 4, 0, 1, 5, 6, 7, 8], [3, 4, 0, 1, 2, 5, 6, 7, 8], [4, 0, 1, 2, 3, 5, 6, 7, 8]] and specified point=5. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=5. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

75. A Fiber Equals a Left Coset of the Same Point Stabilizer

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(10)={0,…,9}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 0, 6, 7, 8, 9], [2, 3, 4, 5, 0, 1, 6, 7, 8, 9], [3, 4, 5, 0, 1, 2, 6, 7, 8, 9], [4, 5, 0, 1, 2, 3, 6, 7, 8, 9], [5, 0, 1, 2, 3, 4, 6, 7, 8, 9]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Use orbit_point=5. Give (orbit_point, representative, fiber, left_coset, equal, certificate).

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-coset-fiber-bijection · candidate

76. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1}, total action_table=[[0, 1], [1, 0]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=1. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

77. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1], other_point=2. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

78. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

79. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3], other_point=4. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

80. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3, 4], other_point=5. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

81. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2}, total action_table=[[0, 1, 2], [1, 0, 2]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=0. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

82. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

83. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

84. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 0, 5], [2, 3, 4, 0, 1, 5], [3, 4, 0, 1, 2, 5], [4, 0, 1, 2, 3, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

85. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 0, 6], [2, 3, 4, 5, 0, 1, 6], [3, 4, 5, 0, 1, 2, 6], [4, 5, 0, 1, 2, 3, 6], [5, 0, 1, 2, 3, 4, 6]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3, 4], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

86. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3}, total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

87. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1], other_point=2. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

88. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 0, 4, 5], [2, 3, 0, 1, 4, 5], [3, 0, 1, 2, 4, 5]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=1. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

89. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 0, 5, 6], [2, 3, 4, 0, 1, 5, 6], [3, 4, 0, 1, 2, 5, 6], [4, 0, 1, 2, 3, 5, 6]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1], other_point=0. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

90. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 0, 6, 7], [2, 3, 4, 5, 0, 1, 6, 7], [3, 4, 5, 0, 1, 2, 6, 7], [4, 5, 0, 1, 2, 3, 6, 7], [5, 0, 1, 2, 3, 4, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3, 4], other_point=7. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

91. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4}, total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=1. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

92. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=5. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

93. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 0, 4, 5, 6], [2, 3, 0, 1, 4, 5, 6], [3, 0, 1, 2, 4, 5, 6]] and specified point=3. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2], other_point=4. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

94. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 0, 5, 6, 7], [2, 3, 4, 0, 1, 5, 6, 7], [3, 4, 0, 1, 2, 5, 6, 7], [4, 0, 1, 2, 3, 5, 6, 7]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

95. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 0, 6, 7, 8], [2, 3, 4, 5, 0, 1, 6, 7, 8], [3, 4, 5, 0, 1, 2, 6, 7, 8], [4, 5, 0, 1, 2, 3, 6, 7, 8], [5, 0, 1, 2, 3, 4, 6, 7, 8]] and specified point=1. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3, 4], other_point=2. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

96. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5}, total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]] and specified point=2. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0], other_point=3. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

97. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6}, total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]] and specified point=0. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1], other_point=1. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

98. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]], identity=0, point carrier Fin(8)={0,…,7}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 0, 4, 5, 6, 7], [2, 3, 0, 1, 4, 5, 6, 7], [3, 0, 1, 2, 4, 5, 6, 7]] and specified point=6. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1], other_point=7. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

99. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], identity=0, point carrier Fin(9)={0,…,8}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 0, 5, 6, 7, 8], [2, 3, 4, 0, 1, 5, 6, 7, 8], [3, 4, 0, 1, 2, 5, 6, 7, 8], [4, 0, 1, 2, 3, 5, 6, 7, 8]] and specified point=5. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3], other_point=6. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate

100. A Proper Sample or Mixed Point Binding Does Not Supply the Theorem Certificate

Use complete group table=[[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1], [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]], identity=0, point carrier Fin(10)={0,…,9}, total action_table=[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 0, 6, 7, 8, 9], [2, 3, 4, 5, 0, 1, 6, 7, 8, 9], [3, 4, 5, 0, 1, 2, 6, 7, 8, 9], [4, 5, 0, 1, 2, 3, 6, 7, 8, 9], [5, 0, 1, 2, 3, 4, 6, 7, 8, 9]] and specified point=4. Row g/column h gives g*h, and action row g/column x gives g*x. Certify every group/action axiom, then enumerate all group elements with the same action and point binding. Free, faithful or transitive action is not required. Proper nonempty unique sampled_elements=[0, 1, 2, 3, 4], other_point=5. Give (sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary).

The fixed No withholds a theorem certificate from a proper sample or mixed point binding. It does not deny that the sample image may equal the full orbit or that two point stabilizers may coincide.

Reviewed step-by-step derivation

Orbit-stabilizer theorem · qf-mod41-orbitstab-binding-boundary · candidate