On finite groups with non-nilpotent subgroups

被引：2

作者：

Lu, Jiakuan ^{[1
]}

Meng, Wei ^{[2
]}

机构：

[1] Guangxi Normal Univ, Sch Math & Stat, Guilin 541004, Guangxi, Peoples R China

[2] Yunnan Minzu Univ, Sch Math & Comp Sci, Kunming 650031, Yunnan, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2016年 / 179卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Non-nilpotent subgroups; Non-normal subgroups; Solvable groups;

D O I：

10.1007/s00605-014-0712-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a finite group G , let l(G) denote the number of conjugacy classes of non-normal non-nilpotent subgroups of G . In this paper, we show that every finite group G satisfying l(G) <vertical bar pi(G)vertical bar is solvable, and for a finite non-solvable group l(G) <vertical bar pi(G)vertical bar if and only if or SL(2,5).

引用

页码：99 / 103

页数：5

共 11 条

[1]

[Anonymous], 1968, Finite Groups

[2]

Belonogov V.A., 1986, MAT SBORNIK, V131, P225

[3]

Huppert B., 1967, GRUND MATH WISS, V134

[4]

Janko, 1962, MATH Z, V79, P422, DOI [10.1007/BF01193133, DOI 10.1007/BF01193133]

[5] Finite groups with non-nilpotent maximal subgroups [J].

Lu, Jiakuan ;

Pang, Linna ;

Zhong, Xianggui .

MONATSHEFTE FUR MATHEMATIK, 2013, 171 (3-4) :425-431

[6] Lower bounds on conjugacy classes of non-nilpotent subgroups in a finite group [J].

Meng, Wei ;

Lu, Jiakuan .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (03)

[7]

Pazderski G, 1963, MATH NACHR, V26, P307

[8]

Robinson D., 1996, GRADUATE TEXTS MATH

[9]

ROSE JS, 1965, J LONDON MATH SOC, V40, P348

[10] FINITE INSOLUBLE GROUPS WITH NILPOTENT MAXIMAL SUBGROUPS [J].

ROSE, JS .

JOURNAL OF ALGEBRA, 1977, 48 (01) :182-196

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