Strong power automorphism

Definition
An automorphism of a group is termed a strong power automorphism if it is a defining ingredient::power automorphism and its inverse is also a power automorphism.

Facts

 * For a finite group, and more generally, a periodic group, any power automorphism is a strong power automorphism.
 * The identity map in any group, and the inverse map in an abelian group, are strong power automorphisms.
 * A strong power automorphism must send any element of infinite order to itself or its inverse.

Stronger properties

 * Weaker than::Strong universal power automorphism

Weaker properties

 * Stronger than::Strong monomial automorphism
 * Stronger than::Monomial automorphism
 * Stronger than::Power automorphism
 * Stronger than::Normal automorphism
 * Stronger than::Weakly normal automorphism