[Merged by Bors] - feat(GroupTheory/SpecificGroups/AlternatingGroup): subgroups of index 2 of Equiv.Perm#21190
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AntoineChambert-Loir wants to merge 16 commits intomasterfrom
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[Merged by Bors] - feat(GroupTheory/SpecificGroups/AlternatingGroup): subgroups of index 2 of Equiv.Perm#21190AntoineChambert-Loir wants to merge 16 commits intomasterfrom
AntoineChambert-Loir wants to merge 16 commits intomasterfrom
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PR summary 9880f01586
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.GroupTheory.SpecificGroups.Alternating | 948 | 951 | +3 (+0.32%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.GroupTheory.SpecificGroups.Alternating |
3 |
Declarations diff
+ alternatingGroup.index_eq_two
+ alternatingGroup_le_of_index_le_two
+ eq_alternatingGroup_of_index_eq_two
+ eq_bot_of_card_le_two
+ index_eq_one
+ instance : (alternatingGroup α).Characteristic
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
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).
Delete the property that the alternating subgroup is characteristic. I'll prove it later from the results here. (Either in this PR or in a subsequent one).
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I've been able to golf |
alreadydone
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(note that |
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urkud
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This PR/issue depends on: |
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Thanks 🎉
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| simp_rw [mem_top, Nat.card_eq_fintype_card]; rfl | ||
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| @[nontriviality] | ||
| theorem index_eq_one [Subsingleton α] : (alternatingGroup α).index = 1 := by |
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Suggested change
| theorem index_eq_one [Subsingleton α] : (alternatingGroup α).index = 1 := by | |
| theorem alternatingGroup.index_eq_one [Subsingleton α] : (alternatingGroup α).index = 1 := by |
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| open Subgroup Group | ||
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| /-- The alternating group is the only subgroup of index 2 of the permutation group -/ |
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I'd add a period after these full sentences in docstrings. (2 more below)
Suggested change
| /-- The alternating group is the only subgroup of index 2 of the permutation group -/ | |
| /-- The alternating group is the only subgroup of index 2 of the permutation group. -/ |
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🚀 Pull request has been placed on the maintainer queue by alreadydone. |
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Thanks! bors d+ |
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✌️ AntoineChambert-Loir can now approve this pull request. To approve and merge a pull request, simply reply with |
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bors r+
Le 31 janvier 2025 14:58:35 GMT+01:00, "mathlib-bors[bot]" ***@***.***> a écrit :
…✌️ AntoineChambert-Loir can now approve this pull request. To approve and merge a pull request, simply reply with `bors r+`. More detailed instructions are available [here](https://bors.tech/documentation/getting-started/#reviewing-pull-requests).
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… 2 of Equiv.Perm (#21190) A subgroup of index 2 of `Equiv.Perm α`is equal to `alternatingGroup α`, a subgroup of index at most 2 contains it.
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Pull request successfully merged into master. Build succeeded: |
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@AntoineChambert-Loir You seem to have merged this PR without responding to @alreadydone's comments. Can you open a new PR with those changes? |
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* factorial-dvd-int: (143 commits) Apply suggestions from code review feat(Factorial): k! divides the product of any k successive integers feat(CategoryTheory): creation of finite limits (#21320) chore: update Mathlib dependencies 2025-02-01 (#21328) chore(GroupTheory/SpecificGroups/Alternating.lean): follow last minute review of JX (#21314) feat: `‖x‖ₑ.toNNReal = ‖x‖₊` (#21306) chore: cleanup imports in Archive/IfNormalization (#21318) doc: fix several typos (#21315) feat(CategoryTheory): transfer being iso along an iso in the arrow category (#21310) chore: delete declarations deprecated between 2024-01 and 2024-07 (#21271) feat(Analysis/Normed/Module/Dual): polar in a normed space as a submodule (#20084) chore(Data/ZMod/Basic): split `ZMod.valMinAbs` off (#21308) feat(GroupTheory/Perm/Centralizer): study the centralizer of a permutation (#17522) feat(RingTheory/LocalRing): `IsLocalRing` for subrings (#21168) chore: update Mathlib dependencies 2025-02-01 (#21312) chore: update Mathlib dependencies 2025-01-31 (#21311) feat: generalize `mem_dite` to `Membership α β` (#21262) feat: Lemmas for some monomial orders (#16177) feat(CategoryTheory): the localized category is monoidal (#12728) feat: add function log⁺ (=positive part of the logarithm) and prove standard estimates (#21289) feat(RingTheory/WittVector): ring of Witt vectors is p-adically complete (#21295) feat(GroupTheory/GroupAction/Blocks): more on blocks (#21284) fix(FieldTheory/KrullTopology): make `krullTopology_discreteTopology_of_finiteDimensional` universe polymorphic (#21299) feat(RingTheory/Artinian): integral non-zero-divisors are units over artinian rings (#21199) refactor(Topology/Gluing): simplify definition of `TopCat.GlueData.Rel` (#20653) feat(RingTheory/PowerSeries): binomial series (#20192) chore(Mathlib/RingTheory/MvPolynomial): rename MonomiaOrder.lCoeff to MonomialOrder.leadingCoeff (#21290) chore (RingTheory/HahnSeries): fix names that use coeff (#21279) feat: let `notation3` distinguish `Prop` vs `Type _ ` vs `Sort _` (#21233) chore(MeasureTheory/Function/StronglyMeasurable): split Basic into Basic and AEStronglyMeasurable (#21273) feat(CategoryTheory): the monoidal category structure on a localization (#20951) feat(Analysis/Complex/Hadamard): generalize Hadamard's three lines theorem (#15009) feat(Order/CompleteBooleanAlgebra): Himp in terms of sSup (#20328) feat(ENNReal/Basic): add `ofNat_ne_top` and `top_ne_ofNat` (#14486) feat: Function.const as a PartialEquiv (#21137) chore(NonZeroDivisors): don't import rings (#20871) feat(Data/Set/Lattice): insert distributivity with iUnion/iInter (#21267) feat(GroupTheory/SpecificGroups/AlternatingGroup): subgroups of index 2 of Equiv.Perm (#21190) feat(GroupTheory/GroupAction/Transitive): basic results on transitive actions (#21285) perf(MeasureTheory/Function/LpSpace.lean): speed up (#21179) feat(Order): order isomorphisms from `Fin n` for small `n` (#21120) refactor(Topology/Group): turn morphisms in ProfiniteGrp into one field structures (#20740) feat: Sylow's first theorem for elementary `p`-groups (#21072) chore(Submonoid/Membership): don't import `MonoidWithZero` (#20748) refactor(Algebra/Algebra/Pi): cleanup and renaming (#21213) feat(GroupTheory/IndexNormal): subgroups of small index are normal (#21186) feat(Algebra/Group/Action): add definition of equidecomposition (#16936) feat(CategoryTheory/Subpresheaf): equalizer (#21096) feat: add lemmas about products of `Matrix.stdBasisMatrix` (#21204) chore: update Mathlib dependencies 2025-01-31 (#21282) ...
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… 2 of Equiv.Perm (#21190) A subgroup of index 2 of `Equiv.Perm α`is equal to `alternatingGroup α`, a subgroup of index at most 2 contains it.
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A subgroup of index 2 of
Equiv.Perm αis equal toalternatingGroup α,a subgroup of index at most 2 contains it.