Splitting automorphisms of prime order. (Q1878652)

Let \(G\) be a finite group, and \(\sigma\) an automorphism of \(G\) of order \(p\) (an odd prime). If for all \(g\in G\) one has \(gg^\sigma\cdots g^{\sigma^{pd-1}}=1\) with \((6p,d)=1\), then \(G\) is solvable. The paper continues and uses several well-known studies on generalized f.p.f. automorphisms of a group.