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New characterization of S 4(q) by its noncommuting graph

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Abstract

Let G be a nonabelian group, and associate the noncommuting graph ∇(G) with G as follows: the vertex set of ∇(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. Let S 4(q) be the projective symplectic simple group, where q is a prime power. We prove that if G is a group with ∇(G) ≅ ∇(S 4(q)) then G ≅ S 4(q).

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Authors and Affiliations

  1. Suzhou University, Suzhou, Jiangsu, China

    Liangcai Zhang & Wujie Shi

  2. Chongqing University, Shapingba, Chongqing, P. R. China

    Liangcai Zhang & Wujie Shi

Authors
  1. Liangcai Zhang
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  2. Wujie Shi
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Corresponding author

Correspondence to Wujie Shi.

Additional information

Original Russian Text Copyright © 2009 Zhang L. and Shi W.

The authors were supported by the NNSF of China (Grant 10871032), SRFDP of China (Grant 20060285002), and a subproject of the NNSF of China (Grant 50674008) (Chongqing University, Grants 104207520080834 and 104207520080968).

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Suzhou; Chongqing. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 3, pp. 669–679, May–June, 2009.

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Zhang, L., Shi, W. New characterization of S 4(q) by its noncommuting graph. Sib Math J 50, 533–540 (2009). https://doi.org/10.1007/s11202-009-0059-7

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  • DOI: https://doi.org/10.1007/s11202-009-0059-7

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