∀ {G : Type u_1} [inst : Group G] {p : ℕ} (P : Sylow p G) (hP : (↑P).normalizer ≤ Subgroup.centralizer ↑P)
  [inst_1 : Fact (Nat.Prime p)] [inst_2 : Finite (Sylow p G)] [inst_3 : (↑P).FiniteIndex] (g : G) (hg : g ∈ P),
  (MonoidHom.transferSylow P hP) g = ⟨g ^ (↑P).index, ⋯⟩