A Criterion on the Finite p-Nilpotent Groups

被引：3
|
作者：
Xiangyang XU [1 ]
Yangming LI [2 ]
机构：
[1] Department of Mathematics,Nanchang Normal University
[2] Department of Mathematics,Guangdong University of Education
来源：
Journal of Mathematical Research with Applications | 2019年 / 39卷 / 03期
基金：
中国国家自然科学基金;
关键词：
p-nilpotent group; k-th center of a group; s-semipermutable subgroup;
D O I：
暂无
中图分类号：
O152.1 [有限群论];
学科分类号：
摘要：
Let G be a finite group. Suppose that H is a subgroup of G. We say that H is s-semipermutable in G if HG;= G;H for any Sylow p-subgroup G;of G with（p, |H|） = 1,where p is a prime dividing the order of G. We give a p-nilpotent criterion of G under the hypotheses that some subgroups of G are s-semipermutable in G. Our result is a generalization of the famous Burnside’s p-nilpotent criterion.
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页码：254 / 258
页数：5
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