A power automorphism of a group is an automorphism that takes each subgroup of the group to within itself.
It is worth noting that the power automorphism of an infinite group may not restrict to an automorphism on each subgroup. For instance, the automorphism on rational numbers that send each number to its double is a power automorphism even though it does not restrict to an automorphism on each subgroup.
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. The power automorphisms of a group form a subgroup of the whole automorphism group. This subgroup is denoted as ${\displaystyle Pot(G)}$ where ${\displaystyle G}$ is the group.