EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 251–263 (2015)

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Simple groups with the same prime graph as $^2D_n(q)$

Behrooz Khosravi, A. Babai

School of Mathematics, Institute for Research in Fundamental sciences (IPM), Tehran, Iran; Department of Mathematics, University of Qom, Qom, Iran

Abstract: In 2006, Vasil'ev posed the problem: \emph{Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphic nonabelian finite simple groups with the same graphs of primes? Conjecture: $k=5$.} In 2013, Zvezdina, confirmed the conjecture for the case when one of the groups is alternating. We continue this work and determine all nonabelian simple groups having the same prime graphs as the nonabelian simple group $^2D_n(q)$.

Keywords: prime graph; simple group; Vasil'ev conjecture

Classification (MSC2000): 20D05; 20D60

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Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

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