Complete Point Stabilizers, Subgroup Closure and Membership Boundaries

1. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1} and total action_table=[[0, 1], [1, 0]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

2. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

3. The Point Stabilizer Enumerates Every Fixing Group Element

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} and total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

4. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

5. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

6. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 0, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

7. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

8. The Point Stabilizer Enumerates Every Fixing Group Element

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} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

9. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

10. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

11. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

12. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

13. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

14. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

15. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

16. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

17. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

18. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

19. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

20. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

21. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

22. The Point Stabilizer Enumerates Every Fixing Group Element

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6} and total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

23. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

24. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=5. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

25. The Point Stabilizer Enumerates Every Fixing Group Element

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Give (point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-stabilizer-of-point · candidate

26. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1} and total action_table=[[0, 1], [1, 0]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

27. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

28. Identity, Product and Inverse Closure Certify the Full 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} and total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

29. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

30. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

31. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 0, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

32. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

33. Identity, Product and Inverse Closure Certify the Full 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} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

34. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

35. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

36. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

37. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

38. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

39. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

40. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

41. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

42. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

43. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

44. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

45. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

46. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

47. Identity, Product and Inverse Closure Certify the Full Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6} and total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

48. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

49. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=5. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

50. Identity, Product and Inverse Closure Certify the Full 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Give (stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-subgroup-certificate · candidate

51. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1} and total action_table=[[0, 1], [1, 0]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

52. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Test group_element=1. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

53. Fixing This Point Is Exactly Membership in Its 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} and total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=2. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

54. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

55. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Test group_element=4. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

56. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 0, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=1. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

57. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

58. Fixing This Point Is Exactly Membership in Its 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} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

59. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

60. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

61. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

62. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Test group_element=2. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

63. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

64. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

65. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Test group_element=2. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

66. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Test group_element=1. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

67. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Test group_element=1. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

68. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Test group_element=1. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

69. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

70. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Test group_element=1. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

71. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

72. Fixing This Point Is Exactly Membership in Its Stabilizer

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6} and total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

73. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Test group_element=2. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

74. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=5. Test group_element=3. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

75. Fixing This Point Is Exactly Membership in Its 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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Test group_element=0. Give (group_element, point, image, fixes_point, in_stabilizer).

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-membership-audit · candidate

76. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(2)={0,…,1} and total action_table=[[0, 1], [1, 0]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Compare other_point=1. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

77. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Compare other_point=2. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

78. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and total action_table=[[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 0, 1, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

79. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Compare other_point=4. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

80. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Compare other_point=5. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

81. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(3)={0,…,2} and total action_table=[[0, 1, 2], [1, 0, 2]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=0. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

82. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 2, 0, 3], [2, 0, 1, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

83. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 3, 0, 4], [2, 3, 0, 1, 4], [3, 0, 1, 2, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

84. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

85. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

86. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(4)={0,…,3} and total action_table=[[0, 1, 2, 3], [1, 0, 2, 3]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

87. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 2, 0, 3, 4], [2, 0, 1, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Compare other_point=2. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

88. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Compare other_point=1. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

89. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Compare other_point=0. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

90. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Compare other_point=7. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

91. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(5)={0,…,4} and total action_table=[[0, 1, 2, 3, 4], [1, 0, 2, 3, 4]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Compare other_point=1. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

92. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 2, 0, 3, 4, 5], [2, 0, 1, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Compare other_point=5. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

93. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=3. Compare other_point=4. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

94. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

95. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=1. Compare other_point=2. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

96. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1], [1, 0]], identity=0, point carrier Fin(6)={0,…,5} and total action_table=[[0, 1, 2, 3, 4, 5], [1, 0, 2, 3, 4, 5]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=2. Compare other_point=3. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

97. Point Stabilizers May Agree without Becoming Orbits or Kernels

Use complete group table=[[0, 1, 2], [1, 2, 0], [2, 0, 1]], identity=0, point carrier Fin(7)={0,…,6} and total action_table=[[0, 1, 2, 3, 4, 5, 6], [1, 2, 0, 3, 4, 5, 6], [2, 0, 1, 3, 4, 5, 6]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=0. Compare other_point=1. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

98. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=6. Compare other_point=7. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

99. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=5. Compare other_point=6. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate

100. Point Stabilizers May Agree without Becoming Orbits or Kernels

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} and 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]]. Group row g/column h gives g*h; action row g/column x gives g*x. Every group and action axiom must qualify before the stabilizer is computed. Specified point=4. Compare other_point=5. Give (point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary).

The fixed No withholds identification of stabilizer, orbit and action kernel as concepts. It does not negate same_stabilizer or rule out equality of particular sets.

Reviewed step-by-step derivation

Stabilizer of a finite group action · qf-mod40-stabilizer-point-boundary · candidate