Cover-avoidance properties and the structure of finite groups

被引：88

作者：

Guo, XY ^{[1
]}

Shun, KP

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Shanxi, Peoples R China

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2003年 / 181卷 / 2-3期

关键词：

D O I：

10.1016/S0022-4049(02)00327-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We call a subgroup A of a finite group G a CAP-subgroup of G if for any chief factor H/K of G, we have H boolean AND A = K boolean AND A or HA = KA. In this paper, some characterizations for a finite group to be solvable are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups be CAP-subgroups. We also determine the p-solvability and p-nilpotency of finite groups by considering their CAP-subgroups. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：297 / 308

页数：12

共 10 条

[1] [Anonymous], REND SEM MAT U PADOV
[2] [Anonymous], 1976, CANAD MATH B, DOI DOI 10.4153/CMB-1976-033-5
[3] Gaschutz W., 1962, ARCH MATH, V13, P418
[4] COVER-AVOID SUBGROUPS IN FINITE SOLVABLE GROUPS
GILLAM, JD
[J]. JOURNAL OF ALGEBRA, 1974, 29 (02) : 324 - 329
[5] Gorenstein D., 1980, Finite groups, V2
[6] Huppert B., 1967, Endliche Gruppen I, VI
[7] Kurzweil H, 1967, ENDLICHE GRUPPEN
[8] ROBINSON D J S, 1993, COURSE THEORY GROUPS
[9] FINITE INSOLUBLE GROUPS WITH NILPOTENT MAXIMAL SUBGROUPS
ROSE, JS
[J]. JOURNAL OF ALGEBRA, 1977, 48 (01) : 182 - 196
[10] SCHALLER KU, 1971, THESIS U KIEL

← 1 →