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On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups

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Abstract

We study finite groups with the following property (*): All subgroups of odd index are pronormal. Suppose that G has a normal subgroup A with property (*), and the Sylow 2-subgroups of G/A are self-normalizing. We prove that G has property (*) if and only if so does NG(T)/T, where T is a Sylow 2-subgroup of A. This leads to a few results that can be used for the classification of finite simple groups with property (*).

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Authors and Affiliations

  1. University of Science and Technology of China, Hefei, P. R. China

    W. Guo & D. O. Revin

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, Ekaterinburg, Russia

    N. V. Maslova

  3. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    D. O. Revin

Authors
  1. W. Guo
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  2. N. V. Maslova
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  3. D. O. Revin
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Correspondence to W. Guo.

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Original Russian Text © 2018 Guo W., Maslova N.V., and Revin D.O.

Hefei; Ekaterinburg; Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 4, pp. 773–790, July–August, 2018; DOI: 10.17377/smzh.2018.59.404.

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Guo, W., Maslova, N.V. & Revin, D.O. On the Pronormality of Subgroups of Odd Index in Some Extensions of Finite Groups. Sib Math J 59, 610–622 (2018). https://doi.org/10.1134/S0037446618040043

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  • DOI: https://doi.org/10.1134/S0037446618040043

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