Characterization of the alternating group by its non-commuting graph

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• 作者：Alireza Abdollahi^a ; ^b ; ^{a.abdollahi@math.ui.ac.ir} ; Hamid Shahverdi^a ; ^{hamidshahverdi@gmail.com}
• 关键词：20D06 ; 20D60
• 刊名：Journal of Algebra
• 出版年：2012
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：1 May, 2012
• 卷：357
• 期：Complete
• 页码：203-207
• 文件大小：125 K

摘要

Let G be any non-abelian group and be its center. The non-commuting graph of G is the simple graph whose vertex set is , with two vertices x and y adjacent whenever . We prove that if is isomorphic to the non-commuting graph of the alternating group (), then . This result together with a recent one due to Solomon and Woldar gives a complete positive answer to a conjecture proposed in [A. Abdollahi, S. Akbari, H.R. Maimani, Non-commuting graph of a group, J. Algebra 298 (2006) 468-492]: If S is any finite non-abelian simple group such that for some group G, then .