Normaliser

From Citizendium
Revision as of 12:24, 29 December 2008 by imported>Richard Pinch (subpages)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to 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, the normaliser of a subgroup of a group (mathematics) is the set of all group elements which map the given subgroup to itself by conjugation.

Formally, for H a subgroup of a group G, we define

A subgroup of G is normal in G if its normaliser is the whole of G.

The normaliser of the trivial subgroup is the whole group G.