中文摘要：

设G为有限群，H是G的子群。称H是G的S-拟正规子群，如果对G的任意Sylow子群P，有HP=PH；称H是G的S-拟正规嵌入子群，若H的Sylow子群为G的某个S-拟正规子群的Sylow子群；称H是G的C＊-正规子群，如果G有正规子群K使得G=HKH．满足H∩K在G中是S-拟正规嵌入的。设d是P-群P的最小生成元个数。考虑P的d个极大子群构成的集合Md（P）={P1,…，Pd）且使得它们的交是P的Frattini子群φ（P）。对Md（P）中的群在满足C＊-正规假设条件下群的结构进行了研究，并推广了最近的一些结论。

英文摘要：

Let G be a finite group and H a subgroup of G. It says that H is an S -quasinormal subgroup of G if HP = PH for any Sylow subgroup P of G ; H is an S -quasinormally embedded subgroup of G if every Sylow subgroup of H is a Sylow subgroup of some S -quasinormal subgroup of G ; H is a C＊-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H n K is S -quasinormally embedded in G. Let d be the smallest generator number of a p -group P. Consider a set Md （P） = { P1 ,…, Pd } of maximal subgroups of P such that ∩i=1^dPi= φ（P） . The aim is to investigate the structure of finite group G under the assumption that all members in Md（P） are C＊-normal in G , and generalizes some recent results.