Centralizer of involution

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This article is about a term related to the Classification of finite simple groups

Definition

Symbol-free definition

A subgroup of a group is termed a centralizer of involution if it occurs as the centralizer (in the whole group) of some involution (an involution here is an element of order two).

Definition with symbols

A subgroup $H$ of a group $G$ is termed a centralizer of involution if $H=C_{G}(t)$ for some $t\neq e$ such that $t^{2}=e$.