The diameter of the commuting graph of a finite group with trivial centre

被引：46
作者：
Morgan, G. L. [1 ]
Parker, C. W. [2 ]
机构：
[1] Univ Western Australia, Sch Math & Stat M019, Crawley, WA 6009, Australia
[2] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
来源：
JOURNAL OF ALGEBRA | 2013年 / 393卷
关键词：
Finite group theory; Graph theory; Simple groups; INVOLUTION GRAPHS; COMPONENTS;
D O I：
10.1016/j.jalgebra.2013.06.031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The commuting graph Gamma of a finite group with trivial centre is examined. It is shown that the connected components of Gamma have diameter at most 10. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：41 / 59
页数：19
相关论文
共 29 条
[1]   On the diameters of commuting graphs [J].
Akbari, S. ;
Mohammadian, A. ;
Radjavi, H. ;
Raja, P. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (01) :161-176
[2]  
[Anonymous], 1968, Finite Groups
[3]  
ASCHBACHER M, 1976, NAGOYA MATH J, V63, P1
[4]  
ASCHBACHER M, 2000, CAMBRIDGE STUD ADV M, V10
[5]   Commuting involution graphs for sporadic simple groups [J].
Bates, C. ;
Bundy, D. ;
Hart, S. ;
Rowley, P. .
JOURNAL OF ALGEBRA, 2007, 316 (02) :849-868
[6]   Commuting involution graphs in special linear groups [J].
Bates, C ;
Bundy, D ;
Perkins, S ;
Rowley, P .
COMMUNICATIONS IN ALGEBRA, 2004, 32 (11) :4179-4196
[7]   TRANSITIVE GROUP OF EVEN ORDER, WHEREIN EACH INVOLUTION FIXES EXACTLY ONE POINT [J].
BENDER, H .
JOURNAL OF ALGEBRA, 1971, 17 (04) :527-&
[8]   The Magma algebra system .1. The user language [J].
Bosma, W ;
Cannon, J ;
Playoust, C .
JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265
[9]   ON GROUPS OF EVEN ORDER [J].
BRAUER, R ;
FOWLER, KA .
ANNALS OF MATHEMATICS, 1955, 62 (03) :565-583
[10]   Non-abelian Sylow subgroups of finite groups of even order [J].
Chigira, N ;
Iiyori, N ;
Yamaki, H .
INVENTIONES MATHEMATICAE, 2000, 139 (03) :525-539
123