The bracket on a group given by commutator.

instance commutatorElement {G : Type u_1} [Group G] : Bracket G G

The commutator of two elements g₁ and g₂.

theorem commutatorElement_def {G : Type u_1} [Group G] (g₁ g₂ : G) : ⁅g₁, g₂⁆ = g₁ * g₂ * g₁⁻¹ * g₂⁻¹