show · group.conjugacy_class all knowls · up · search:

If $G$ is a group and $x\in G$, the conjugacy class of $x$ is the set $\{gxg^{-1}\mid g\in G\}$. These sets partition $G$, and the set of conjugacy classes is denoted by $G^\natural$.

Since conjugation by fixed $g\in G$ is an automorphism of a $G$, all conjugate elements have the same order in the group.

Knowl status:
  • Review status: reviewed
  • Last edited by David Roe on 2020-10-13 18:18:20
Referred to by:
History: (expand/hide all)