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Theorems · Definition · group theory

Sylow.comapOfInjective

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

The preimage of a Sylow subgroup under an injective homomorphism is a Sylow subgroup.

Defined in
Mathlib.GroupTheory.Sylow
Cited by
1 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupGroup
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Around this declaration

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

Sylow.subtype · cited by 10Sylow.subtypeSylow.coe_comapOfInjective · cited by 0Sylow.coe_comapOfInjectiveDFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupMonoidHom · cited by 3629MonoidHomSubgroup · cited by 3593SubgroupMonoidHom.range · cited by 314MonoidHom.rangeSylow · cited by 103SylowSylow.toSubgroup · cited by 86Sylow.toSubgroupIsPGroup.ker_isPGroup_of_injective · cited by 3IsPGroup.ker_isPGroup_of_…Sylow.comapOfKerIsPGroup · cited by 1Sylow.comapOfKerIsPGroupSylow.comapOfInjectiveCITED BYCITES

Cites9

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Cited by2

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