# conjugacy class

Let $G$ a group, and consider its operation (action) on itself give by conjugation, that is, the mapping

 $(g,x)\mapsto gxg^{-1}$

Since conjugation is an equivalence relation, we obtain a partition of $G$ into equivalence classes, called conjugacy classes. So, the conjugacy class of $X$ (represented $C_{x}$ or $C(x)$ is given by

 $C_{x}=\{y\in X:y=gxg^{-1}\mbox{for some }g\in G\}$
Title conjugacy class ConjugacyClass1 2013-03-22 14:01:39 2013-03-22 14:01:39 drini (3) drini (3) 5 drini (3) Definition msc 20E45