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Finite Groups with Three Nonconjugate Maximal Formational Subgroups

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Abstract

A constructive description is obtained for the hereditary \(Z\)-saturated formations \(\mathfrak{F}\) of finite solvable groups containing every solvable group possessing three pairwise nonconjugate maximal subgroups belonging to \(\mathfrak{F}\). It is proved that a finite group \(G\) is supersolvable if it has three pairwise nonconjugate supersolvable maximal subgroups and its commutator subgroup \(G'\) is nilpotent.

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Notes

  1. Translator’s note: \(C_G(H/K)\) stands for the centralizer of the quotient \(H/K\) in \(G\).

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Authors and Affiliations

  1. Francisk Skorina Gomel State University, Gomel, 246019, Belarus

    A. F. Vasil’ev, V. I. Murashka & A. K. Furs

Authors
  1. A. F. Vasil’ev
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  2. V. I. Murashka
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  3. A. K. Furs
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Correspondence to A. F. Vasil’ev.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 354-364 https://doi.org/10.4213/mzm13324.

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Vasil’ev, A.F., Murashka, V.I. & Furs, A.K. Finite Groups with Three Nonconjugate Maximal Formational Subgroups. Math Notes 111, 356–363 (2022). https://doi.org/10.1134/S0001434622030038

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