Involution

This article defines a property of elements in groups

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 $x\neq e$ and $x^{2}=e$.

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

Relation with other properties

Stronger properties

• Central involution

Weaker properties

• Rational element
• Strongly real element
• Real element

Related group properties

• Elementary abelian 2-group is a group in which all the non-identity elements are involutions.