conjugacy class

English

Noun

conjugacy class (plural conjugacy classes)

1. (algebra) A subset of a group which is an equivalence class in the quotient set of the group divided by conjugation as equivalence relation.

   For a given element $x$ of some group $G$, its conjugacy class $x^{G}$ is $\{y\in G|\exists g\in G:g^{-1}xg=y\}$.

   If a group acts on itself through conjugation, then its orbits are its conjugacy classes and its stabilizer subgroups are its centralizers.