Finite groups with graphs containing no triangles

被引：27

作者：

Fang, M ^{[1
]}

Zhang, P ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

来源：

JOURNAL OF ALGEBRA | 2003年 / 264卷 / 02期

基金：

美国国家科学基金会;

关键词：

conjugacy classes; graph; Frobenius group;

D O I：

10.1016/S0021-8693(03)00142-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a non-Abelian finite group, Gamma(G) the attached graph related to its conjugacy classes. The aim of this paper is to prove that the symmetric group S-3, the dihedral group D-5, the three pairwise non-isomorphic non-Abelian groups of order 12, and the non-Abelian group T-21 of order 21, is the complete list of all G such that Gamma(G) contains no triangles. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：613 / 619

页数：7

共 10 条

[1]

ADAMI S, 1996, REND ISTIT LOMBARDO, V130, P295

[2] ON A GRAPH RELATED TO CONJUGACY CLASSES OF GROUPS [J].

BERTRAM, EA ;

HERZOG, M ;

MANN, A .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1990, 22 :569-575

[3] ON THE LENGTH OF THE CONJUGACY CLASSES OF FINITE-GROUPS [J].

CHILLAG, D ;

HERZOG, M .

JOURNAL OF ALGEBRA, 1990, 131 (01) :110-125

[4] ON THE DIAMETER OF A GRAPH RELATED TO CONJUGACY CLASSES OF GROUPS [J].

CHILLAG, D ;

HERZOG, M ;

MANN, A .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1993, 25 :255-262

[5]

Curtis C. W., 1981, METHODS REPRESENTATI, VI

[6] PRIME FACTORS OF CONJUGACY-CLASS LENGTHS AND IRREDUCIBLE CHARACTER-DEGREES IN FINITE SOLUBLE GROUPS [J].

DOLFI, S .

JOURNAL OF ALGEBRA, 1995, 174 (03) :749-752

[7] ARITHMETICAL CONDITIONS ON THE LENGTH OF THE CONJUGACY CLASSES OF A FINITE-GROUP [J].

DOLFI, S .

JOURNAL OF ALGEBRA, 1995, 174 (03) :753-771

[8] A PROOF OF SZEPS CONJECTURE ON NONSIMPLICITY OF CERTAIN FINITE-GROUPS [J].

FISMAN, E ;

ARAD, Z .

JOURNAL OF ALGEBRA, 1987, 108 (02) :340-354

[9] THE S-3-CONJECTURE FOR SOLVABLE-GROUPS [J].

KNORR, R ;

LEMPKEN, W ;

THIELCKE, B .

ISRAEL JOURNAL OF MATHEMATICS, 1995, 91 (1-3) :61-76

[10]

Lu ZQ, 2001, ALGEBR COLLOQ, V8, P55

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