conjugacy class

Let G a group, and consider its operationMathworldPlanetmath (action) on itself give by conjugationMathworldPlanetmath, that is, the mapping


Since conjugation is an equivalence relationMathworldPlanetmath, we obtain a partitionMathworldPlanetmathPlanetmath of G into equivalence classesMathworldPlanetmath, called conjugacy classesMathworldPlanetmathPlanetmath. So, the conjugacy class of X (represented Cx or C(x) is given by

Cx={yX:y=gxg-1for some gG}
Title conjugacy class
Canonical name ConjugacyClass1
Date of creation 2013-03-22 14:01:39
Last modified on 2013-03-22 14:01:39
Owner drini (3)
Last modified by drini (3)
Numerical id 5
Author drini (3)
Entry type Definition
Classification msc 20E45