有限群的可解性

doi:10.3969/j.issn.0253-2778.2015.06.003

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (6): 443-448.DOI: 10.3969/j.issn.0253-2778.2015.06.003

• 论著 • 上一篇

有限群的可解性

张丽，李保军

1.中国科学技术大学数学系，安徽合肥 230026；2.成都信息工程学院应用数学学院，四川成都 610225

收稿日期:2015-01-21 修回日期:2015-04-13 接受日期:2015-04-13 出版日期:2015-04-13 发布日期:2015-04-13

Solubility of finite groups

ZHANG Li, LI Baojun

1.Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; 2.College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China

Received:2015-01-21 Revised:2015-04-13 Accepted:2015-04-13 Online:2015-04-13 Published:2015-04-13
Contact: ZHANG Li
About author:ZHANG Li (corresponding author), female, born in 1991, PhD. Research field: group theory.
Supported by:
Supported by a NNSF of China (11371335,11471055).

摘要/Abstract

摘要： 设H是有限群G的一个p子群. ①H在G中满足Φ*性质，如果对G的任一非可解Frattini主因子L/K，|G：NG(K(H∩L))|是p的方幂；②H称为在G中Φ*嵌入的，如果存在G的次正规子群T使得HT是G的S拟正规子群且H∩T≤S，其中,S≤H在G中满足Φ*性质.这里主要利用Φ*嵌入子群进一步研究有限群的结构，特别地，得到了群G可解的一些新判别准则.

关键词: p子群, Φ*性质, Φ*嵌入, Sylow子群

Abstract: Let H be a p-subgroup of G. Then: ① H satisfies Φ*-property in G if H is a Sylow subgroup of some subnormal subgroup of G and for any non-solubly-Frattini chief factor L/K of G, |G:NG(K(H∩L))| is a power of p; ② H is called Φ*-embedded in G if there exists a subnormal subgroup T of G such that HT is S-quasinormal in G and H∩T≤S, where S≤H satisfies Φ*-property in G. Here Φ*-embedded subgroups were used to study the structure of finite groups and, in particular, some new characterizations for a group G to be soluble are obtained.

Key words: p-subgroups, Φ*-property, Φ*-embedded, Sylow subgroup

中图分类号:

张丽，李保军. 有限群的可解性[J]. 中国科学技术大学学报, 2015, 45(6): 443-448.

ZHANG Li, LI Baojun. Solubility of finite groups[J]. Journal of University of Science and Technology of China, 2015, 45(6): 443-448.

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有限群的可解性

Solubility of finite groups

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