2-极大子群的C-正规性与p-幂零群  

C-normality of 2-maximal subgroups and p-nilpotent groups

作　　者：花子建 何立国[1] HUA Zijian;HE Liguo(School of Science,Shenyang University of Technology,Shenyang 110870,China)

机构地区：[1]沈阳工业大学理学院,辽宁沈阳110870

出　　处：《高师理科学刊》2022年第6期1-3,共3页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(12171058)。

摘　　要：利用子群的C-正规性,讨论了Sylow子群的每个2-极大子群的C-正规性对有限群p-幂零性的影响,证明了:(1)设p是|G|的最小素因子,如果N_(G)(P)是p-幂零的且群G的Sylow p-子群的每个2-极大子群在G中C-正规,那么G是p-幂零的;(2)设N■G,使得G/N是p-幂零的,p是|G|的最小素因子,如果N_(G)(P)是p-幂零的且群N的Sylow p-子群的每个2-极大子群在G中C-正规,那么G是p-幂零的.Using the C-normality of subgroups,the influence of C-normality of each 2-maximal subgroup of Sylow subgroups on the p-nilpotency of finite groups is discussed.It is proved that:(1)Let p be the minimum prime factor of G,ifN_(G)(P) is p-nilpotent and every 2-maximal subgroup of Sylow subgroup of group G is C-normal in G,then G is p-nilpotent;(2)Let N■G,such that G/N is p-nilpotent,p is the minimum prime factor of |G|,if N_(G)(P) is p-nilpotent and every 2-maximal subgroup of Sylow subgroups of N is C-normal in G,then G is p-nilpotent.

关 键 词：C-正规子群 P-幂零群 2-极大子群 有限群 

分 类 号：O152[理学—数学]