Theorems · Theorem · group theory
Sylow.finite_of_injective
∀ {p : ℕ} {G : Type u_1} [inst : Group G] {H : Type u_2} [inst_1 : Group H] {f : H →* G},
Function.Injective ⇑f → ∀ [Finite (Sylow p G)], Finite (Sylow p H)If f : H →* G is injective, then Finite (Sylow p G) implies Finite (Sylow p H).
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
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- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Finitestatement and proof · cited by 3,029
- Sylowstatement and proof · cited by 103
- IsPGroup.ker_isPGroup_of_injectiveproof · cited by 3
- Sylow.finite_of_ker_is_pGroupproof · cited by 2
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