Weakly power automorphisms of groups. Issue 1 (2nd January 2018) - De Falco, M.; de Giovanni, F.; Musella, C.; Sysak, Y. P.
ABSTRACT: An automorphism α of a group G is called a weakly power automorphism if it maps every non-periodic subgroup of G onto 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 group G of derived length at most 3 are power automorphisms, i.e. they fix all subgroups of G . 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.