Subgroup.focalSubgroupOf.pow_index_surjective

∀ {G : Type u_1} [inst : Group G] {p : ℕ} [Fact (Nat.Prime p)] (P : Sylow p G) [(↑P).FiniteIndex],
  Function.Surjective fun y => y ^ (↑P).index

The power map y ↦ y^n is surjective on P/P* because gcd(n, p) = 1.

Defined in: Mathlib.GroupTheory.Focal
Cited by: 1 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group Fact Subgroup.FiniteIndex

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