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.
