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Abstract

In this paper, the structure of finite groups in which maximal subgroups of some Sylow subgroups have a

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-soluble or

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-nilpotent supplement, where

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is a partition of the set of all prime numbers, is investigated. Some solubility,

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-solubility and

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-nilpotency criteria leading to some significant improvements of earlier results are given.

Keywords

Finite group / Supplementation /

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-Solubility')">

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-Solubility /

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-Nilpotency')">

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-Nilpotency

References

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[5] Kamornikov, S.F., Tyutyanov, V.N.: On two problems from “The Kourovka Notebook”. Trudy Inst. Mat. i Mekh. UrO RAN 138(1):98–102 (2021). (in Russian)

[6] Liu A-M, Guo W, Safonova IN, Skiba AN. G \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G$$\end{document}-covering subgroup systems for some classes of -soluble groups. J. Algebra, 2021, 585: 280-293,

[7] Mazurov VD, Khukhro EI. . Unsolved Problems in Group Theory: The Kourovka Notebook, 2018 19 Novosibirsk Russian Academy of Sciences, Siberian Branch, Institute of Mathematics

[8] Skiba AN. On -subnormal and -permutable subgroups of finite groups. J. Algebra, 2015, 436: 1-16,

Funding

Universitat de Valencia