局部子群的性质对群构造的影响

J4 ›› 2011, Vol. 46 ›› Issue (12): 51-54.

局部子群的性质对群构造的影响

普昭年¹,汤菊萍²,顾春华³

1. 河西学院数学与统计学院, 甘肃张掖 734000;2. 扬州大学数学科学学院, 江苏扬州 225002;
3.江阴职业技术学院, 江苏江阴 214405

收稿日期:2011-03-08 出版日期:2011-12-20 发布日期:2011-12-24
作者简介:普昭年(1964- ),男,本科,副教授,研究方向为有限群论. Email:puzhaonian@163.com
基金资助:
国家自然科学基金资助项目(10901133); 江苏省高校自然科学基金资助项目(09KJB110009)

The influence of the properties of local subgroups on the structure of finite groups

PU Zhao-Nian¹, TANG Ju-Ping², GU Chun-Hua³

1. School of Mathematics and Statistics, Hexi University, Zhangye 734000, Gansu, China;
2. School of Mathematic Sciences,Yangzhou University,Yangzhou 225002, Jiangsu, China;
3.Jiangyin Polytechnic College, Jiangyin 214405, Jiangsu, China

Received:2011-03-08 Online:2011-12-20 Published:2011-12-24

摘要/Abstract

摘要：

称子群H在群G中M-可补, 若存在子群B,使得G=HB, 且对于H的任意极大子群H1, 都有H1B为G的真子群。将子群的性质局部化,在群G的Sylow子群的正规化子中来考察子群的M-可补性,对有限群构造作进一步探索得到p幂零、超可解的一些新结果。

关键词: M-可补子群; s-拟正规;p-幂零群;Sylow子群;正规化子

Abstract:

The properties of the subgroups have been localized in order to consider the M-supplementation of NG(P), where P is the Sylow p-subgroup of G, and some results about p-nilpotency and supersolvablity have been obtained.

Key words: M-supplemented subgroups; s-quasinormal; p-nilpotent; Sylow subgroups; normalizer

普昭年1,汤菊萍2,顾春华3. 局部子群的性质对群构造的影响[J]. J4, 2011, 46(12): 51-54.

PU Zhao-Nian1, TANG Ju-Ping2, GU Chun-Hua3. The influence of the properties of local subgroups on the structure of finite groups[J]. J4, 2011, 46(12): 51-54.

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed