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This article is cited in 2 scientific papers (total in 2 papers)
Finite Groups with Three Nonconjugate Maximal Formational Subgroups
A. F. Vasil'ev, V. I. Murashka, A. K. Furs Gomel State University named after Francisk Skorina
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.
Keywords:
finite group, maximal subgroup, $Z$-saturated formation, formation with the Belonogov property, formation with the Kegel property, supersolvable group.
Received: 18.10.2021 Revised: 30.11.2021
Citation:
A. F. Vasil'ev, V. I. Murashka, A. K. Furs, “Finite Groups with Three Nonconjugate Maximal Formational Subgroups”, Mat. Zametki, 111:3 (2022), 354–364; Math. Notes, 111:3 (2022), 356–363
Linking options:
https://www.mathnet.ru/eng/mzm13324https://doi.org/10.4213/mzm13324 https://www.mathnet.ru/eng/mzm/v111/i3/p354
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