# Extended automorphism group

From Groupprops

## Definition

Let be a group. The **extended automorphism group** of is the group comprising all the automorphisms and anti-automorphisms of . An anti-automorphism is a map such that for all .

The extended automorphism group is either equal to the automorphism group or contains the automorphism group as a subgroup of index two. Equality holds if and only if the group is an abelian group.