# Invariant subset

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Invariant subset.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Invariant_subset&oldid=37452

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article