Invariant subset

2020 Mathematics Subject Classification: Primary: 20E45 [MSN][ZBL]

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 classes of $G$. An invariant sub-semi-group is a sub-semi-group that is at the same time an invariant subset.