Automorphisms of finite order of nilpotent groups IV

  • B.A.F. Wehrfritz

    Queen Mary University of London, UK

Abstract

Let be an automorphism of finite order of the nilpotent group of class and and positive integers with . Consider the two (not usually homomorphic) maps and of given by

We prove that the subgroups

of all have finite exponent bounded in terms of , and only. This yields alternative proofs of the theorem of [4] and its related bounds.

Cite this article

B.A.F. Wehrfritz, Automorphisms of finite order of nilpotent groups IV. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 61–68

DOI 10.4171/RSMUP/136-6