Recognition by noncommuting graph of finite simple groups <italic>L</italic><sub>4</sub>(<italic>q</italic>)

doi:10.1007/s11464-010-0085-6

Front Math Chin

2011, Vol. 6

Issue (1) : 1-16 https://doi.org/10.1007/s11464-010-0085-6

RESEARCH ARTICLE

Recognition by noncommuting graph of finite simple groups L₄(q)

M. AKBARI¹, M. KHEIRABADI¹, A. R. MOGHADDAMFAR^1,2(

)

1. Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran; 2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

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Abstract

Let G be a nonabelian group. We define the noncommuting graph ?(G) of G as follows: its vertex set is G\Z(G), the set of non-central elements of G, and two different vertices x and y are joined by an edge if and only if x and y do not commute as elements of G, i.e., [x,y]≠1. We prove that if L ∈ {L₄(7), L₄(11), L₄(13), L₄(16), L₄(17)} and G is a finite group such that ?(G)??(L), then G?L.

Keywords noncommuting graph spectrum prime graph projective special linear group L₄(q) recognition by noncommuting graph

Corresponding Author(s): MOGHADDAMFAR A. R.,Email:moghadam@kntu.ac.ir, moghadam@mail.ipm.ir

Issue Date: 01 February 2011

Cite this article:

M. AKBARI,M. KHEIRABADI,A. R. MOGHADDAMFAR. Recognition by noncommuting graph of finite simple groups L₄(q)[J]. Front Math Chin, 2011, 6(1): 1-16.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0085-6
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I1/1

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