Theorems · Theorem · group theory
IsPGroup.ker_isPGroup_of_injective
∀ {p : ℕ} {G : Type u_1} [inst : Group G] {K : Type u_2} [inst_1 : Group K] {ϕ : K →* G},
Function.Injective ⇑ϕ → IsPGroup p ↥ϕ.ker- Defined in
- Mathlib.GroupTheory.PGroup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.kerstatement · cited by 212
- IsPGroupstatement and proof · cited by 96
- MonoidHom.ker_eq_botproof · cited by 10
- IsPGroup.of_botproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Sylow.exists_comap_eq_of_injectiveproof · cited by 2
- IsPGroup.comap_of_injectiveproof · cited by 1
- Sylow.comapOfInjectiveproof · cited by 1
- Sylow.finite_of_injectiveproof · cited by 0