conjugacy class

Two elements g and g of a group G are said to be conjugate if there exists hG such that g=hgh-1. Conjugacy of elements is an equivalence relationMathworldPlanetmath, and the equivalence classesMathworldPlanetmath of G are called conjugacy classesMathworldPlanetmath.

Two subsets S and T of G are said to be conjugate if there exists gG such that


In this situation, it is common to write gSg-1 for T to denote the fact that everything in T has the form gsg-1 for some sS. We say that two subgroupsMathworldPlanetmathPlanetmath of G are conjugate if they are conjugate as subsets.

Title conjugacy class
Canonical name ConjugacyClass
Date of creation 2013-03-22 12:18:09
Last modified on 2013-03-22 12:18:09
Owner djao (24)
Last modified by djao (24)
Numerical id 5
Author djao (24)
Entry type Definition
Classification msc 20A05
Synonym conjugate
Synonym conjugate set
Synonym conjugate subgroup
Related topic ConjugacyClassFormula