Cofactorial automorphism

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.

Stronger properties

 * Weaker than::Inner automorphism
 * Weaker than::Stability automorphism

Weaker properties

 * Stronger than::Automorphism

Related subgroup properties

 * Cofactorial automorphism-invariant subgroup
 * Sub-cofactorial automorphism-invariant subgroup
 * Subgroup-cofactorial automorphism-invariant subgroup