Strong power automorphism

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Definition

An automorphism of a group is termed a strong power automorphism if it is a 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.

Relation with other properties

Stronger properties

• Strong universal power automorphism

Weaker properties

• Strong monomial automorphism
• Monomial automorphism
• Power automorphism
• Normal automorphism
• Weakly normal automorphism