Theorems · Theorem · group theory
Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOf
∀ {G : Type u_1} [inst : Group G] {p : ℕ} [Fact (Nat.Prime p)] (P : Sylow p G) [inst_2 : (↑P).FiniteIndex],
((↑P).transferFocal.domRestrict P).ker = (↑P).focalSubgroupOf- Defined in
- Mathlib.GroupTheory.Focal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Factstatement and proof · cited by 2,726
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.Primestatement and proof · cited by 2,059
- one_powproof · cited by 521
- MonoidHom.kerstatement · cited by 212
- QuotientGroup.mkproof · cited by 196
- Subgroup.indexproof · cited by 150
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.extproof · cited by 108
- Sylowstatement and proof · cited by 103
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.ker_transferFocal_inf_eq_focalSubgroupproof · cited by 1