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Quasirecognition of One Class of Finite Simple Groups by the Set of Element Orders

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Abstract

We prove that a finite group, having the same set of element orders as a finite simple group L and the prime graph with at least three connected components, possesses a (unique) nonabelian composition factor which is isomorphic to L, unless L is isomorphic to the alternating group of degree 6.

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Authors and Affiliations

  1. South Ural State University, Chelyabinsk

    O. A. Alekseeva

  2. Institute of Mathematics and Mechanics, Ekaterinburg

    A. S. Kondrat'ev

Authors
  1. O. A. Alekseeva
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  2. A. S. Kondrat'ev
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Alekseeva, O.A., Kondrat'ev, A.S. Quasirecognition of One Class of Finite Simple Groups by the Set of Element Orders. Siberian Mathematical Journal 44, 195–207 (2003). https://doi.org/10.1023/A:1022931316876

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