Theorems · Theorem · group theory
Subgroup.focalSubgroupOf_eq_closure
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), H.focalSubgroupOf = Subgroup.closure {g | ∃ x ∈ H, ∃ u, ↑g = ⁅x, u⁆}- Defined in
- Mathlib.GroupTheory.Focal
- Cited by
- 1 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- Subgroup.mapproof · cited by 301
- Subgroup.closurestatement and proof · cited by 196
- Subgroup.subtypeproof · cited by 185
- commutatorElementstatement · cited by 41
- MonoidHom.map_closureproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.commutator_le_focalSubgroupOfproof · cited by 1