center — Mathlib

English

In a commutative group, ((S.leftInvEquiv hS).symm x) equals the inverse of x: ((S.leftInvEquiv hS).symm x : M) = (x : M)^{-1}.

Русский

В коммутативной группе выражение ((S.leftInvEquiv hS).symm x) равно обратному к x.

LaTeX

$$$ ((S.leftInvEquiv hS).symm x : M) = (x : M)^{-1} $$$

Lean4

/-- The center of a semigroup `M` is the set of elements that commute with everything in `M` -/
@[to_additive /-- The center of an additive semigroup `M` is the set of elements that commute with
    everything in `M` -/
    ]
def center : Subsemigroup M where
  carrier := Set.center M
  mul_mem' := Set.mul_mem_center

Похожие утверждения