Cofactorial automorphism

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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Definition

For a finite group

An automorphism \sigma of a finite group G is termed a cofactorial automorphism for G if every prime dividing the order of \sigma (viewed as an element of the automorphism group of G) also divides the order of G.

For a periodic group

An automorphism \sigma of a periodic group G is termed a cofactorial automorphism for G if every prime dividing the order of \sigma equals the order of some non-identity element of G.

For a group with elements of infinite order

If the group has any element of infinite order, then every automorphism of the group is considered to be a cofactorial automorphism.

Relation with other properties

Stronger properties

Weaker properties

Related subgroup properties