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.

引用

页码：254 / 258

页数：5

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