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Theorems · Theorem · group theory

Sylow.coe_mapSurjective

∀ {p : ℕ} {G : Type u_1} [inst : Group G] [inst_1 : Finite G] {G' : Type u_2} [inst_2 : Group G'] {f : G →* G'}
  (hf : Function.Surjective ⇑f) [inst_3 : Fact (Nat.Prime p)] (P : Sylow p G),
  ↑(Sylow.mapSurjective hf P) = Subgroup.map f ↑P
Defined in
Mathlib.GroupTheory.Sylow
Cited by
2 results in Mathlib
Foundations
Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupFiniteGroupFact
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Around this declaration

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

Sylow.mapSurjective_surjective · cited by 2Sylow.mapSurjective_surje…isZGroup_of_coprime · cited by 1isZGroup_of_coprimeDFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupMonoidHom · cited by 3629MonoidHomSubgroup · cited by 3593SubgroupFinite · cited by 3029FiniteFact · cited by 2726FactNat.Prime · cited by 2059Nat.PrimeSubgroup.map · cited by 301Subgroup.mapSylow · cited by 103SylowSylow.toSubgroup · cited by 86Sylow.toSubgroupSylow.mapSurjective · cited by 4Sylow.mapSurjectiveSylow.coe_mapSurjectiveCITED BYCITES

Cites11

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Cited by2

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