Influence of weakly H-subgroups of minimal subgroups on the structure of finite groups

Abstract

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H) \ Hg H for all g in G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and  H \ K is an H-subgroup in G. In this paper, we use weakly H-subgroup condition on minimal subgroups to study the structure of the finite group G. Some earlier results are improved and extend.