Strong power automorphism

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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

Weaker properties