Finite groups with a system of generalized central elements

Abstract

Let H be a normal subgroup of a finite group G. A number of authors have investigated the structure of G under the assumption that all minimal or maximal subgroups in Sylow subgroups of H are well-situated in G. A general approach to the results of that kind is proposed in this article. The author has found the conditions for p-elements of H under which G-chief p-factors of H are F-central in G.