弱s-置换嵌入子群对p-幂零群的影响

广西师范大学学报（自然科学版） ›› 2010, Vol. 28 ›› Issue (3): 29-32.

弱s-置换嵌入子群对p-幂零群的影响

李长稳¹, 於遒²

1.徐州师范大学数学科学学院,江苏徐州221116;
2.淮海工学院理学院,江苏连云港222001

收稿日期:2010-04-25 出版日期:2010-09-20 发布日期:2023-02-06
通讯作者: 於遒(1968—),男,江苏淮安人,淮海工学院副教授,博士。E-mail:property1111@yahoo.com.cn
基金资助:
国家自然科学基金资助项目(10771180);徐州师范大学科研基金资助项目(09XLB01)

Influence of Weakly s-permutably Embedded Subgroups on p-nilpotent Groups

LI Chang-wen¹, YU Qiu²

1. School of Mathematical Science,Xuzhou Normal University,Xuzhou Jiangsu 221116,China;
2. School of Science,Huaihai Institute of Technology,Lianyuangang Jiangsu222001,China

Received:2010-04-25 Online:2010-09-20 Published:2023-02-06

摘要/Abstract

摘要： 称群G的一个子群H在G中弱s-置换嵌入的,如果存在G的一个次正规子群T和包含在H中的G的一个s-置换嵌入子群H_se,使得G=HT且H∩T≤H_se。利用弱s-置换嵌入子群的性质给出了p-幂零群的一些新刻画。

关键词: 弱s-置换嵌入, p-幂零, Sylow p-子群

Abstract: A subgroup H of a group G is said to be weakly s-permutably embedded in G if there are a subnormal subgroup T ofG and an s-permutably embedded subgroup H_se of G contained in H such that G=HT and H∩T≤H_se.By using the property ofweakly s-permutably embedded groups,some criterions of p-nilpotency offinite groups are obtained.

Key words: weakly s-permutably embedded, p-nilpotent, Sylow p-subgroup

中图分类号:

O152

李长稳, 於遒. 弱s-置换嵌入子群对p-幂零群的影响[J]. 广西师范大学学报（自然科学版）, 2010, 28(3): 29-32.

LI Chang-wen, YU Qiu. Influence of Weakly s-permutably Embedded Subgroups on p-nilpotent Groups[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 29-32.

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