Extensions of several coprime results to good action case

摘要

Let G and A be groups where A acts on G by automorphisms. We say "the action of A on G is good" if the equality H = H, BC-H (B) holds for any subgroup B of A and for any B-invariant subgroup H of G. It is straightforward that every coprime action is a good action. In this work, we extend some results due to Ward, Gross, Shumyatsky, Jabara and Meng and Guo under coprime action to good action.