Centralizer of involution

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 $$t \ne e$$ such that $$t^2 = e$$.