Power automorphism

Symbol-free definition
An automorphism of a group is termed a power automorphism if it satisfies the following equivalent conditions:


 * It is a power map in the sense that it takes each element to a power of itself
 * It takes each subgroup to within itself.

Stronger properties

 * Weaker than::Uniform power automorphism:
 * Weaker than::Strong power automorphism: A strong power automorphism is a power automorphism whose inverse is also a power automorphism.

Weaker properties

 * Stronger than::Power endomorphism
 * Stronger than::Monomial automorphism
 * Stronger than::Weakly normal automorphism