Outer automorphism group

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This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Let G be a group. The outer automorphism group of G, denoted \operatorname{Out}(G), is defined as the quotient group of the automorphism group \operatorname{Aut}(G) by the inner automorphism group \operatorname{Inn}(G).

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.