Strong power automorphism

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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.


  • 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

Weaker properties