# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 25 results; page 1/1. ## Question 24951: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0026`; number: 24951 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0026/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0026.json) ## Question 24952: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0027`; number: 24952 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0027/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0027.json) ## Question 24953: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0028`; number: 24953 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0028/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0028.json) ## Question 24954: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0029`; number: 24954 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0029/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0029.json) ## Question 24955: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0030`; number: 24955 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0030/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0030.json) ## Question 24956: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0031`; number: 24956 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0031/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0031.json) ## Question 24957: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0032`; number: 24957 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0032/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0032.json) ## Question 24958: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0033`; number: 24958 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0033/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0033.json) ## Question 24959: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0034`; number: 24959 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0034/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0034.json) ## Question 24960: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0035`; number: 24960 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0035/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0035.json) ## Question 24961: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0036`; number: 24961 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0036/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0036.json) ## Question 24962: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0037`; number: 24962 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0037/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0037.json) ## Question 24963: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0038`; number: 24963 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0038/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0038.json) ## Question 24964: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0039`; number: 24964 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0039/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0039.json) ## Question 24965: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0040`; number: 24965 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0040/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0040.json) ## Question 24966: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0041`; number: 24966 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0041/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0041.json) ## Question 24967: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0042`; number: 24967 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0042/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0042.json) ## Question 24968: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0043`; number: 24968 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0043/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0043.json) ## Question 24969: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0044`; number: 24969 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0044/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0044.json) ## Question 24970: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0045`; number: 24970 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0045/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0045.json) ## Question 24971: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0046`; number: 24971 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0046/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0046.json) ## Question 24972: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0047`; number: 24972 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0047/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0047.json) ## Question 24973: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0048`; number: 24973 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0048/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0048.json) ## Question 24974: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0049`; number: 24974 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0049/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0049.json) ## Question 24975: The Identity Preimage of a Qualified Homomorphism Is a Normal Subgroup - ID: `q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0050`; number: 24975 - Processing: second_context_reviewed - MKO: [mko-finite-group-homomorphism-kernel](/en/mko/mko-finite-group-homomorphism-kernel/) - Family: [qf-mod45-kernel-normal-subgroup-audit](/en/explore/?family=qf-mod45-kernel-normal-subgroup-audit) - Batch: [batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations](/en/explore/?batch=batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations) - [Derivation](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0050/) / [Markdown](/en/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0050.json)