# 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.