Even automorphism

From Groupprops
Jump to: navigation, search

Definition

An automorphism of a finite group is termed an even automorphism if it is an even permutation.

For any finite group, the even automorphisms form a subgroup of the group of all automorphisms. This subgroup is either the whole group, or is a subgroup of index two.

Note that the definition is vacuous over infinite groups since an infinite group has no non-identity finitary automorphism.

Relation with other properties

Stronger properties

Facts