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On the existence of Carter subgroups

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Abstract

In terms of normal series of a finite group, the existence criterion of a Carter subgroup is obtained. An example showing that the criterion cannot be reformulated in terms of composition factors is given. In conclusion, Carter subgroups in almost simple groups are classified.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Koptyuga 4, Novosibirsk, 630090, Russia

    E. P. Vdovin

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  1. E. P. Vdovin
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Published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2007, Vol. 13, No. 1.

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Vdovin, E.P. On the existence of Carter subgroups. Proc. Steklov Inst. Math. 257 (Suppl 1), S195–S203 (2007). https://doi.org/10.1134/S008154380705015X

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  • DOI: https://doi.org/10.1134/S008154380705015X

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