Theorems · Theorem · group theory
Subgroup.isPerfect_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, Group.IsPerfect ↥H ↔ ⁅H, H⁆ = H- Defined in
- Mathlib.GroupTheory.IsPerfect
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- MonoidHom.range_eq_mapproof · cited by 37
- Subgroup.range_subtypeproof · cited by 28
- Group.IsPerfectstatement · cited by 17
- Subgroup.map_subtype_injproof · cited by 11
- Subgroup.map_subtype_commutatorproof · cited by 7
- Group.isPerfect_defproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Group.IsPerfect.mapproof · cited by 1
- Subgroup.commutator_eq_selfproof · cited by 1