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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 16, Issue 6


Simple groups are characterized by their non-commuting graphs

Ronald M. Solomon / Andrew J. Woldar
Published Online: 2013-08-01 | DOI: https://doi.org/10.1515/jgt-2013-0021


The non-commuting graph of a finite group G is a highly symmetrical object (indeed, embeds in ), yet its complexity pales in comparison to that of G. Still, it is natural to seek conditions under which G can be reconstructed from . Surely some conditions are necessary, as is evidenced by the minuscule example . A conjecture made in [J. Algebra 298 (2006), 468–492], commonly referred to as the AAM Conjecture, proposes that the property of being a nonabelian simple group is sufficient. In [Sib. Math. J. 49 (2008), no. 6, 1138–1146], this conjecture is verified for all sporadic simple groups, while in [J. Algebra 357 (2012), 203–207], it is verified for the alternating groups. In this paper we verify it for the simple groups of Lie type, thereby completing the proof of the conjecture.

About the article

Received: 2013-04-18

Revised: 2013-05-06

Published Online: 2013-08-01

Published in Print: 2013-11-01

Citation Information: Journal of Group Theory, Volume 16, Issue 6, Pages 793–824, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2013-0021.

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