Weakly power automorphisms of groups.

An automorphismαof a groupGis called aweakly power automorphismif it maps every non-periodic subgroup ofGonto itself. The aim of this paper is to investigate the behavior of weakly power automorphisms. In particular, among other results, it is proved that all weakly power automorphisms of a soluble non-periodic groupGof derived length at most 3 are power automorphisms, i.e. they fix all subgroups ofG. This result is best possible, as there exists a soluble non-periodic group of derived length 4 admitting a weakly power automorphism, which is not a power automorphism. [ABSTRACT FROM PUBLISHER]