Solubility of finite groups admitting a fixed-point-free automorphism of order rst, II

Abstract

This paper, which is one of a series of four, contributes to the proof of the following THEOREM. A finite group admitting a coprime fixed-point-free automorphism a of order rst (r, s and t distinct primes) is soluble. Here we prove that in a minimal counterexample to the above theorem the set of a-invariant Sylow p-subgroups P, such that Cp(~')~l for all c~l, generate a soluble subgroup.