View source for Invariant subset

{{TEX|done}}{{MSC|20E45}}

''of a group $G$''

A subset $H$ of $G$ the property that if it contains some element $h$ then it contains all [[conjugate elements]] of $h$ in $G$, that is, all elements of the form $g^{-1}hg$ for $g \in G$; hence, a subset which is a union of [[conjugacy class]]es of $G$. An invariant sub-semi-group is a sub-semi-group that is at the same time an invariant subset.