Aufl�sbare Gruppen auf denen nicht aufl�sbare Gruppen operieren

Abstract

Let G be a finite solvable group and A a subgroup of Aut G such that ¦G¦ and ¦A¦ are coprime. A conjecture states: The nilpodent length of G is bounded by terms depending only on A and the fixed point group GA={g∈G¦gA=g}. For abelian, nilpotent or solvable A various bounds are known. In this paper we study the nonsolvable case and prove the conjecture for wide classes of nonsolvable groups A, especially in the fixed point free case GA=1.