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This article is cited in 3 scientific papers (total in 3 papers)
Finite Factorizable Groups with $\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors
V. S. Monakhov Gomel State University named after Francisk Skorina
Abstract:
We study a finite factorized group $G=AB$ in the case when the factors $A$ and $B$ can be connected to $G$ by a chain of subgroups with prime indices, and either all subgroups with nilpotent derived subgroups or all Schmidt subgroups in $A$ and $B$ are supersolvable. Such factorizations cover both the groups that are products of normal supersolvable subgroups and mutually permutable products of supersolvable subgroups. In particular, it follows from the results obtained here that all Schmidt subgroups in products of normal supersolvable subgroups and in mutually permutable products of supersolvable subgroups are supersolvable; however, a nonsupersolvable subgroup with nilpotent derived subgroup can exist.
Keywords:
finite group, supersolvable group, factorized group, Schmidt subgroup.
Received: 11.08.2021 Revised: 13.10.2021
Citation:
V. S. Monakhov, “Finite Factorizable Groups with $\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors”, Mat. Zametki, 111:3 (2022), 403–410; Math. Notes, 111:3 (2022), 407–413
Linking options:
https://www.mathnet.ru/eng/mzm13255https://doi.org/10.4213/mzm13255 https://www.mathnet.ru/eng/mzm/v111/i3/p403
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