In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.
Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis t...Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis the core of H in G.A CSp-group is a group in which every p-subgroup is cp-supplemented.In this paper,we characterize the p-solvability and psupersolvability of groups G with some certain p-subgroups being cp-supplemented.Furthermore,we give some equivalent conditions of CSp-group in p-solvable universe.Finally,we give some criteria of CSp-groups for the direct product of two CSp-groups.Our results extend some recent conclusions.展开更多
基金Foundation item： Supported by the National Nature Science Foundation of China（11071229） Supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions（10KJD110004）
文摘In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.
基金Supported by the National Natural Science Foundation of China(Grant No.12071092)the Science and Technology Program of Guangzhou Municipality(Grant No.201804010088).
文摘Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis the core of H in G.A CSp-group is a group in which every p-subgroup is cp-supplemented.In this paper,we characterize the p-solvability and psupersolvability of groups G with some certain p-subgroups being cp-supplemented.Furthermore,we give some equivalent conditions of CSp-group in p-solvable universe.Finally,we give some criteria of CSp-groups for the direct product of two CSp-groups.Our results extend some recent conclusions.
