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Finite Groups with Formation Subnormal Normalizers of Sylow Subgroups

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Abstract

Let \(\mathfrak{F}\) be a formation. Properties of the class \(\mathrm{w}^{*}\mathfrak{F}\) of all groups \(G\) for which \(\pi(G)\subseteq\pi(\mathfrak{F})\) and the normalizers of all Sylow subgroups are \(\mathfrak{F}\)-subnormal in \(G\) are studied. In particular, it is established that this class is a formation closed with respect to taking Hall subgroups. Hereditary saturated formations \(\mathfrak{F}\) coinciding with \(\mathrm{w}^{*}\mathfrak{F}\) are found.

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Authors and Affiliations

  1. Francisk Skorina Gomel State University, 24019, Gomel, Belarus

    A. F. Vasil’ev & A. G. Koranchuk

  2. Belarusian State University of Transport, 246653, Gomel, Belarus

    T. I. Vasil’eva

Authors
  1. A. F. Vasil’ev
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  2. T. I. Vasil’eva
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  3. A. G. Koranchuk
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Correspondence to A. F. Vasil’ev.

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Vasil’ev, A.F., Vasil’eva, T.I. & Koranchuk, A.G. Finite Groups with Formation Subnormal Normalizers of Sylow Subgroups. Math Notes 108, 661–670 (2020). https://doi.org/10.1134/S0001434620110048

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  • DOI: https://doi.org/10.1134/S0001434620110048

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