Groups admitting a fixed-point-free automorphism of order 2ⁿ

Fletcher Gross

Vol. 24 (1968), No. 2, 269–275

DOI: 10.2140/pjm.1968.24.269

Abstract

Let G be a finite solvable group which admits a fixedpoint-free automorphism of order 2ⁿ. The main result of this paper is that the nilpotent length of G is at most 2n − 2 for n ≧ 2. This is an improvement on earlier results in that no assumptions are made regarding the Sylow subgroups of G.

Mathematical Subject Classification

Primary: 20.40

Milestones

Received: 5 July 1967

Published: 1 February 1968