Outer automorphism group: Difference between revisions
(New page: {{basicdef}} ==Definition== Let <math>G</math> be a group. The '''outer automorphism group''' of <math>G</math>, denoted <math>\operatorname{Out}(G)</math>, is defined as the [[quoti...) |
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* [[Homomorphism from automorphism group of | * [[Homomorphism from automorphism group of connected groupoid to outer automorphism group at a point]] | ||
Latest revision as of 20:31, 6 October 2008
This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition
Let be a group. The outer automorphism group of , denoted , is defined as the quotient group of the automorphism group by the inner automorphism group .
Elements of the outer automorphism group are sometimes termed outer automorphism classes. Each outer automorphism class is a coset of the inner automorphism group -- it is not a single automorphism. Thus, the outer automorphism group is not the set of outer automorphisms.