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Theorems · Definition · group theory

Sylow.comapOfKerIsPGroup

{p : ℕ} →
  {G : Type u_1} →
    [inst : Group G] →
      (P : Sylow p G) →
        {K : Type u_2} → [inst_1 : Group K] → (ϕ : K →* G) → IsPGroup p ↥ϕ.ker → ↑P ≤ ϕ.range → Sylow p K

The preimage of a Sylow subgroup under a p-group-kernel homomorphism is a Sylow subgroup.

Defined in
Mathlib.GroupTheory.Sylow
Cited by
1 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Sylow.comapOfInjective · cited by 1Sylow.comapOfInjectiveSylow.coe_comapOfKerIsPGroup · cited by 0Sylow.coe_comapOfKerIsPGr…Group · cited by 6238GroupMonoidHom · cited by 3629MonoidHomSubgroup · cited by 3593SubgroupMonoidHom.range · cited by 314MonoidHom.rangeMonoidHom.ker · cited by 212MonoidHom.kerSubgroup.comap · cited by 154Subgroup.comapSylow · cited by 103SylowIsPGroup · cited by 96IsPGroupSylow.toSubgroup · cited by 86Sylow.toSubgroupSylow.comapOfKerIsPGroupCITED BYCITES

Cites9

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Cited by2

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