Conjugacy class

Revision as of 12:00, 16 July 2020 by Duck master (talk | contribs) (added more info)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

A conjugacy class is a particular subset of a group.

Let $G$ be a group. Consider the action of $G$ on itself by inner automorphisms. The orbits of $G$ are then called conjugacy classes. By expanding the definition, it is easy to show that two elements $g$ and $g'$ are in the same conjugacy class iff there is an element $x$ such that $g' = x^{-1}gx$.

Two subsets $H$ and $H'$ of $G$ are called conjugate if there exists $\alpha \in G$ for which $H$ is the image of $H'$ under $\text{Int}(\alpha)$.

The character of any group $G$ are constant on conjugacy classes.

This article is a stub. Help us out by expanding it.

See also