Abstract
Let \( \mathfrak{F} \) be a class of groups and let \( G \) be a finite group. We refer to a set \( \Sigma \) of subgroups of \( G \) as a \( G \)-covering subgroup system for a class \( \mathfrak{F} \) if \( G\in\mathfrak{F} \) whenever \( \Sigma\subseteq\mathfrak{F} \). Also, we provide some nontrivial \( G \)-covering subgroup system for the class \( \mathfrak{F} \) of all \( \sigma \)-nilpotent groups.
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Funding
The first author was supported by the Ministry of Education of the Republic of Belarus (Grant no. 20211779). The second author was supported by the RFBR and BRFFR (Project F20R–291).
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 116–122. https://doi.org/10.33048/smzh.2022.63.108
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Kamornikov, S.F., Tyutyanov, V.N. On One Criterion for the \( \sigma \)-Nilpotency of a Finite Group. Sib Math J 63, 97–101 (2022). https://doi.org/10.1134/S0037446622010086
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DOI: https://doi.org/10.1134/S0037446622010086