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数学进展 - 2018, Vol. 47(1): 65-70
研究论文
$p$-幂零群的一个判定准则
A Criterion on the Finite $p$-nilpotent Groups

苏宁1, 李样明2, 王燕鸣1,3
SU Ning1,*, LI Yangming2,*, WANG Yanming1,3,*

1. 中山大学数学学院, 广州, 广东, 510275;
2. 广东第二师范学院数学系, 广州, 广东, 510310;
3. 中山大学岭南学院, 广州, 广东, 510275
1. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, 510275, P. R. China;
2. Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, 510310,P. R. China;
3. Lingnan College, Sun Yat-sen University, Guangzhou, Guangdong, 510275, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 65-70
DOI: 10.11845/sxjz.2016049b


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摘要 设 $G$是一个有限群, $P$ 是$G$的一个Sylow $p$-子群. 在$N_{G}(P)$为$p$-幂零的假设下, 通过假定$P$的一个特殊的子群在$G$中满足覆盖远离性, 本文给出了$G$为$p$-幂零群的一个判定准则.
关键词 $p$-幂零群群的$k$-中心部分覆盖远离子群幂零群的幂零类    
Abstract:Let $G$ be a finite group and $P$ a Sylow \py subgroup of $G$. We give a $p$-nilpotent criterion of $G$ under the hypotheses that $N_{G}(P)$ is \py nilpotent and a particular subgroup of $P$ has the partial cover-avoidance property in $G$.
Key words$p$-nilpotent group    the $k$-th center of a group    the partial CAP-subgroup    the nilpotency class of a nilpotent group
PACS:  O152.1  
通讯作者: E-mail: $*$ suning3@mail.sysu.edu.cn; $**$ liyangming@gdei.edu.cn; $**$*$ stswym@mail.sysu.edu.cn   
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[1] 张丽, 吴珍凤, 郭文彬. 有限群的CAP-拟正规子群[J]. 数学进展, 2017, 46(6): 897-907.
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