Involution

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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 \ne e and x^2 = e.

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

Relation with other properties

Stronger properties

Weaker properties

Related group properties