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 $\mathrm{conj}(G)$.

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

Knowl status:
  • Review status: reviewed
  • Last edited by Jennifer Paulhus on 2022-06-27 18:23:22
Referred to by:
History: (expand/hide all) Differences (show/hide)