Power automorphism

Alternatively, power automorphisms are characterized as automorphisms that send each element of the group to some power of that element.

This explains the choice of the term power.

Here are some facts about the powering index: The group of power automorphisms commutes with the group of inner automorphisms when viewed as subgroups of the automorphism group.

Thus, in particular, power automorphisms that are also inner must arise as conjugations by elements in the second group of the upper central series.

This group theory-related article is a stub.