Involution

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 $$I(G)$$.

Stronger properties

 * Weaker than::Central involution

Weaker properties

 * Stronger than::Rational element
 * Stronger than::Strongly real element
 * Stronger than::Real element

Related group properties

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