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feat(Algebra/Group/Subgroup, GroupTheory/QuotientGroup): strengthen second isomorphism theorem for groups #22650

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@jhanschoo jhanschoo commented Mar 6, 2025

The stronger statement is necessary when we wish that H and H ⊔ N in the statement _ ⧸ N.subgroupOf H ≃* _ ⧸ N.subgroupOf (H ⊔ N) may need to be of a type larger than whichever subgroup H is normal in. Furthermore, this commit adapts some basic results about Normal subgroups to be wrt subgroups of normalizers instead.

Moves:

  • Subgroup.le_normalizer_of_normal -> Subgroup.le_normalizer_of_normal_subgroupOf

The primary reason for introducing this variation is that the existing formulation becomes a pain when quotienting subnormal groups. So suppose my ambient group is G and my normalizer is T : Subgroup G, the result I can get from the existing formulation is something like _ ⧸ (N : T).subgroupOf (H : T) ≃* _ ⧸ (N : T).subgroupOf (H ⊔ N : T), and it is difficult or tedious to recover the desired statement _ ⧸ N.subgroupOf H ≃* _ ⧸ N.subgroupOf (H ⊔ N) from it.

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@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Mar 6, 2025
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github-actions bot commented Mar 6, 2025

PR summary a90a44f49c

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ inf_subgroupOf_normal_of_le_normalizer
+ le_normalizer_mul
+ le_normalizer_of_normal'
+ le_normalizer_of_normal_subgroupOf
+ mul_le_normalizer
+ quotientInfEquivProdNormalizerQuotient
+ setNormalizer_normalizer
+ set_mul_normalizer_comm
+ subgroupOf_sup_normal_of_le_normalizer
+ subset_normalizer_of_normal

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Mar 6, 2025
@Paul-Lez Paul-Lez self-requested a review March 6, 2025 20:26
@jhanschoo jhanschoo force-pushed the diamond_normalizer branch from f0f85a8 to 228298c Compare March 7, 2025 01:07
@jhanschoo jhanschoo force-pushed the diamond_normalizer branch from 228298c to 7114d13 Compare March 7, 2025 02:46
@jhanschoo jhanschoo added the awaiting-author A reviewer has asked the author a question or requested changes label Mar 7, 2025
@jhanschoo jhanschoo changed the title feat(Algebra/Group/Subgroup, GroupTheory/QuotientGroup): strengthen second isomorphism theorem for groups feat(GroupTheory/QuotientGroup): strengthen second isomorphism theorem for groups Mar 7, 2025
@jhanschoo jhanschoo force-pushed the diamond_normalizer branch from 642c8ba to ceaee69 Compare March 7, 2025 13:44
@jhanschoo jhanschoo changed the title feat(GroupTheory/QuotientGroup): strengthen second isomorphism theorem for groups feat(Algebra/Group/Subgroup, GroupTheory/QuotientGroup): strengthen second isomorphism theorem for groups Mar 7, 2025
@jhanschoo jhanschoo removed the awaiting-author A reviewer has asked the author a question or requested changes label Mar 7, 2025
@jhanschoo jhanschoo marked this pull request as ready for review March 7, 2025 13:50
@jhanschoo jhanschoo requested a review from Paul-Lez March 7, 2025 23:37
@Paul-Lez Paul-Lez requested a review from eric-wieser March 10, 2025 18:22
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