Abstract
Let G be a finite group. The spectrum of G is the set ω(G) of orders of all its elements. The subset of prime elements of ω(G) is denoted by π(G). The spectrum ω(G) of a group G defines its prime graph (or Grünberg-Kegel graph) Γ(G) with vertex set π(G), in which any two different vertices r and s are adjacent if and only if the number rs belongs to the set ω(G). We describe all the cases when the prime graphs of a finite simple group and of its proper subgroup coincide.
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Dedicated to the memory of my grandfather Nikolai Yakovlevich Maslov
Original Russian Text © N.V.Maslova, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1.
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Maslova, N.V. On the coincidence of Grünberg-Kegel graphs of a finite simple group and its proper subgroup. Proc. Steklov Inst. Math. 288 (Suppl 1), 129–141 (2015). https://doi.org/10.1134/S0081543815020133
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DOI: https://doi.org/10.1134/S0081543815020133