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New characterizations of \(\sigma \)-nilpotent finite groups

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Abstract

Let \( \sigma =\{\pi _i\mid i\in I\}\) be a partition of the set of all primes. We characterize the class of all \(\sigma \)-nilpotent groups as a hereditary formation \({\mathfrak {F}}\) that contains every group G all whose Sylow subgroups are K-\({\mathfrak {F}}\)-subnormal in their product with the generalized Fitting subgroup \(\mathrm {F}^*(G)\).

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  1. Faculty of Mathematics and Technologies of Programming, Francisk Skorina Gomel State University, 246019, Gomel, Belarus

    Viachaslau I. Murashka & Alexander F. Vasil’ev

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  1. Viachaslau I. Murashka
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  2. Alexander F. Vasil’ev
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Correspondence to Viachaslau I. Murashka.

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This document is the results of the research project funded by Belarusian Republican Foundation for Fundamental Research, Project No. \(\varPhi 20\text {P-}291\).

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I. Murashka, V., F. Vasil’ev, A. New characterizations of \(\sigma \)-nilpotent finite groups. Ricerche mat 73, 611–618 (2024). https://doi.org/10.1007/s11587-021-00627-8

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  • DOI: https://doi.org/10.1007/s11587-021-00627-8

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