On inequalities of subgroups and the structure of finite groups

被引：6

作者：

Li, Jinbao ^{[1
]}

Xie, Fengyan ^{[2
]}

机构：

[1] Chongqing Univ Arts & Sci, Dept Math, Chongqing 402160, Peoples R China

[2] Anyang Normal Univ, Humanist Management Coll, Math & Informat Engn Dept, Anyang 455000, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年

基金：

中国国家自然科学基金;

关键词：

finite groups; weakly Phi-supplemented subgroups; nilpotent groups; supersoluble groups; COMPLEMENTED SUBGROUPS;

D O I：

10.1186/1029-242X-2013-427

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a group and H be a subgroup of G. We say that H is weakly Phi-supplemented in G if G has a subgroup T such that HT = G and H boolean AND T <= Phi (H), where Phi(H) denotes the Frattini subgroup of H. In this paper, properties of this new kind of inequalities of subgroups are investigated and new characterizations of nilpotency and supersolubility of finite groups in terms of the new inequalities are obtained.

引用

页数：7

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