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Paper   IPM / M / 11534
School of Mathematics
  Title:   Recognition by noncommuting graph of finite simple groups L4(q)
  Author(s):  A. R. Moghaddamfar (Joint with M. Akbari and M. Kheirabadi)
  Status:   Published
  Journal: FMC
  Vol.:  6
  Year:  2011
  Pages:   1-16
  Supported by:  IPM
Let G be a non-abelian 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 GL.

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