Solubility of finite groups admitting a fixed-point-free automorphism of order rst. I

Peter John Rowley

Vol. 93 (1981), No. 1, 201–235

DOI: 10.2140/pjm.1981.93.201

Abstract

The ‘fixed-point-free automorphism conjecture’ asserts that if a finite group G admits a fixed-point-free automorphism group A (and, if A is noncyclic, further suppose that (|G|,|A|) = 1), then G is soluble. This paper is the first in a four part series, which considers the above conjecture when A is cyclic of order rst where r, s and t are distinct prime numbers.

Mathematical Subject Classification 2000

Primary: 20D10

Secondary: 20D45

Milestones

Received: 5 January 1979

Revised: 23 June 1980

Published: 1 March 1981