Documentation

Mathlib.Algebra.GroupWithZero.Conj

Conjugacy in a group with zero #

@[simp]
theorem GroupWithZero.isConj_iff₀ {α : Type u_1} [GroupWithZero α] {a b : α} :
IsConj a b ↔ ∃ (c : α), c ≠ 0 ∧ c * a * c⁻¹ = b
theorem GroupWithZero.conj_pow₀ {α : Type u_1} [GroupWithZero α] {s : ℕ} {a d : α} (ha : a ≠ 0) :
(a⁻¹ * d * a) ^ s = a⁻¹ * d ^ s * a