Some open questions in the theory of generalized permutable subgroups

被引：28

作者：

Guo WenBin ^{[1
]}

Xie FengYan ^{[1
]}

Li BaoJun ^{[2
]}

机构：

[1] Xuzhou Normal Univ, Sch Math Sci, Xuzhou 221116, Peoples R China

[2] Chengdu Univ Informat Technol, Sch Math, Chengdu 610225, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2009年 / 52卷 / 10期

基金：

中国国家自然科学基金;

关键词：

finite group; formations; weakly s-supplemented subgroup; maximal subgroup; minimal subgroup; FINITE-GROUPS; SUPPLEMENTED SUBGROUPS; C-NORMALITY;

D O I：

10.1007/s11425-009-0045-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subgroup H of a group G is said to be weakly s-supplemented in G if H has a supplement T in G such that H boolean AND T <= H-sG, where H-sG is the largest s-permutable subgroup of G contained in 1-1. This paper constructs an example to show that the open questions 6.3 and 6.4 in J Algebra, 315: 192-209 (2007) have negative solutions, and shows that in many cases Question 6.4 is positive. A series of known results are unified and generalized.

引用

页码：2132 / 2144

页数：13

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