Conjugacy

From Citizendium
Revision as of 06:13, 18 February 2009 by Chris Day (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

In group theory, conjugacy is the relation between elements of a group that states that one element is the conjugate of the other. This relation is an equivalence relation, and the equivalence classes are the conjugacy classes of the group.

Another way of stating this is to say that conjugation is group action of G on itself, and the conjugacy classes are the orbits of this action.

The conjugacy problem is the decision problem of determining from a presentation of a group whether two elements of the group are conjugate .

The conjugacy problem was identified by Max Dehn in 1911 as one of three fundamental decision problems in group theory; the other two being the group isomorphism problem and the word problem.