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From Groupprops

This article defines a property of elements in groups

Contents 1 Definition 1.1 Symbol-free definition 1.2 Definition with symbols 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties 2.3 Related group properties

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 and x² = 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.