Abstract
We find finite almost simple groups with prime graphs all of whose connected components are cliques, i.e., complete graphs. The proof is based on the following fact, which was obtained by the authors and is of independent interest: the prime graph of a finite simple nonabelian group contains two nonadjacent odd vertices that do not divide the order of the outer automorphism group of this group.
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Original Russian Text © M.R. Zinov’eva, A.S. Kondrat’ev, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 3.
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Zinov’eva, M.R., Kondrat’ev, A.S. Finite almost simple groups with prime graphs all of whose connected components are cliques. Proc. Steklov Inst. Math. 295 (Suppl 1), 178–188 (2016). https://doi.org/10.1134/S0081543816090194
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DOI: https://doi.org/10.1134/S0081543816090194