PlanetMath: conjugacy class

(more info)

Math for the people, by the people.

Main Menu

conjugacy class

(Definition)

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

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

Since conjugation is an equivalence relation, we obtain a partition of into equivalence classes, called conjugacy classes. So, the conjugacy class of (represented or is given by

$\displaystyle C_x=\{y\in X :y=gxg^{-1}$ for some $\displaystyle g\in G\}$

"conjugacy class" is owned by drini. [ full author list (2) | owner history (2) ]

(view preamble)

Log in to rate this entry.
(view current ratings)

Cross-references: equivalence classes, partition, equivalence relation, mapping, conjugation, action, operation, group
There are 6 references to this entry.

This is version 2 of conjugacy class, born on 2003-10-15, modified 2003-10-27.
Object id is 5042, canonical name is ConjugacyClassOfAGroupElement.
Accessed 2759 times total.

Classification:

20E45 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Conjugacy classes)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact