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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2022 Volume 111, Issue 3, Pages 354–364 (Mi mzm13324)

This article is cited in 1 paper

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.

UDC: 512.542

Received: 18.10.2021
Revised: 30.11.2021

DOI: 10.4213/mzm13324


 English version:
Mathematical Notes, 2022, 111:3, 356–363

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© Steklov Math. Inst. of RAS, 2024