Finite Groups with Some C_(p)-Supplemented Subgroups  

作　　者：Yubo LV Yangming LI 

机构地区：[1]School of Mathematical Sciences,Guizhou Normal University,Guizhou 550001,P.R.China [2]School of Mathematics,Guangdong University of Education,Guangdong 510310,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第1期74-82,共9页数学研究及应用（英文版）

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).

摘　　要：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.

关 键 词：c-supplemented subgroup Cp-normal subgroup Cp-supplemented subgroup CSpgroup p-supersolvable group 

分 类 号：O152.1[理学—数学]