# Involution

## Definition

### Symbol-free definition

An element in a group is termed an involution if its order is exactly two, viz if it is a nonidentity element and its square is the identity element.

### Definition with symbols

An element $x$ in a group $G$(with identity element $e$) is termed an involution if $x \ne e$ and $x^2 = e$.

The set of involutions in a group $G$ is denoted by $I(G)$.