On c#-normal subgroups in finite groups  

作　　者：Huaquan WEI Qiao DAI Hualian ZHANG Yubo LV Liying YANG 

机构地区：[1]College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China [2]School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning 530023, China

出　　处：《Frontiers of Mathematics in China》2018年第5期1169-1178,共10页中国高等学校学术文摘·数学（英文）

摘　　要：A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H n K is a CAP-subgroup of G. In this paper, we investigate the influence of fewer c#- normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H n K is a CAP-subgroup of G. In this paper, we investigate the influence of fewer c#- normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.

关 键 词：Finite group c#-normal p-supersolvable P-NILPOTENT SUPERSOLVABLE 

分 类 号：S852.4[农业科学—基础兽医学] TP311.1[农业科学—兽医学]