feat(GroupTheory/PGroup): maximal subgroups of abelian p-groups have index p#41652
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feat(GroupTheory/PGroup): maximal subgroups of abelian p-groups have index p#41652xroblot wants to merge 5 commits into
xroblot wants to merge 5 commits into
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Add three group-theory results: * `QuotientGroup.comapMk'OrderIso'`: the correspondence theorem as an order isomorphism onto `Set.Ici N` (interval-order variant of `comapMk'OrderIso`). * `isCyclic_of_isCoatom_subsingleton`: a group with at most one maximal subgroup is cyclic (only `IsCoatomic (Subgroup G)` needed). * `CommGroup.isSimpleGroup_iff_isCoatom`: a subgroup of a commutative group is maximal iff the quotient by it is simple (group analogue of `isSimpleModule_iff_isCoatom`).
…index p For an abelian `p`-group: * `CommGroup.isCoatom_iff_index_eq_prime`: the maximal subgroups are exactly the subgroups of index `p` (no finiteness needed). * `IsPGroup.exists_index_eq_prime_ne_of_not_isCyclic`: a finite non-cyclic abelian `p`-group has two distinct subgroups of index `p`.
PR summary 13619a6ba5
|
| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.GroupTheory.PGroup | 1139 | 1140 | +1 (+0.09%) |
Import changes for all files
| Files | Import difference |
|---|---|
4 filesMathlib.GroupTheory.Descent Mathlib.GroupTheory.PGroup Mathlib.GroupTheory.Torsion Mathlib.NumberTheory.NumberField.Units.Basic |
1 |
Declarations diff (regex)
+ CommGroup.isCoatom_iff_index_eq_prime
+ CommGroup.isSimpleGroup_iff_isCoatom
+ IsPGroup.exists_index_eq_prime_ne_of_not_isCyclic
+ comapMk'OrderIso'
+ isCyclic_of_isCoatom_subsingleton
You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>
## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.
Declarations diff (Lean)
✅ Lean-aware diff — post-build, computed from the Lean environment (commit
13619a6).
- +10 new declarations
- −0 removed declarations
+AddCommGroup.isSimpleAddGroup_iff_isCoatom
+CommGroup.isCoatom_iff_index_eq_prime
+CommGroup.isSimpleGroup_iff_isCoatom
+IsPGroup.exists_index_eq_prime_ne_of_not_isCyclic
+QuotientAddGroup.comapMk'OrderIso'
+QuotientAddGroup.comapMk'OrderIso'_apply_coe
+QuotientGroup.comapMk'OrderIso'
+QuotientGroup.comapMk'OrderIso'_apply_coe
+isAddCyclic_of_isCoatom_subsingleton
+isCyclic_of_isCoatom_subsingletonNo changes to strong technical debt.
No changes to weak technical debt.
Current commit 13619a6ba5
Reference commit 2800ac2bd3
This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
Add `instance [Finite G] : Finite (Subgroup G)` (and `Finite (AddSubgroup A)` via `to_additive`), and use it to drop the inline `Finite (Subgroup G)` workaround in `IsPGroup.exists_index_eq_prime_ne_of_not_isCyclic`.
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SnirBroshi
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Jul 12, 2026
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Building on the API from #41651, prove some results of the maximal subgroups of an abelian
p-group:CommGroup.isCoatom_iff_index_eq_prime: in an abelianp-group (finite or infinite) the maximal subgroups are exactly the subgroups of indexp.IsPGroup.exists_index_eq_prime_ne_of_not_isCyclic: a finite non-cyclic abelianp-group has two distinct subgroups of indexp.🤖 This PR was extracted from the SKW project by Claude.