Theorems · Theorem · group theory
Sylow.finite_of_ker_is_pGroup
∀ {p : ℕ} {G : Type u_1} [inst : Group G] {H : Type u_2} [inst_1 : Group H] {f : H →* G},
IsPGroup p ↥f.ker → ∀ [Finite (Sylow p G)], Finite (Sylow p H)If the kernel of f : H →* G is a p-group,
then Finite (Sylow p G) implies Finite (Sylow p H).
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.comapproof · cited by 154
- Sylowstatement and proof · cited by 103
- IsPGroupstatement and proof · cited by 96
- Sylow.toSubgroupproof · cited by 86
- Finite.of_injectiveproof · cited by 32
- Sylow.extproof · cited by 3
- Sylow.exists_comap_eq_of_ker_isPGroupproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Sylow.finite_of_finiteIndexproof · cited by 1
- Sylow.finite_of_injectiveproof · cited by 0