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Matematicheskie Zametki, 2022, Volume 111, Issue 3, Pages 403–410
DOI: https://doi.org/10.4213/mzm13255
(Mi mzm13255)
 

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
Full-text PDF (472 kB) Citations (3)
References:
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
English version:
Mathematical Notes, 2022, Volume 111, Issue 3, Pages 407–413
DOI: https://doi.org/10.1134/S0001434622030087
Bibliographic databases:
Document Type: Article
UDC: 517.542
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Mon22}
\by V.~S.~Monakhov
\paper Finite Factorizable Groups with~$\mathbb P$-Subnormal $\mathrm v$-Supersolvable and $\mathrm{sh}$-Supersolvable Factors
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 3
\pages 403--410
\mathnet{http://mi.mathnet.ru/mzm13255}
\crossref{https://doi.org/10.4213/mzm13255}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461270}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 3
\pages 407--413
\crossref{https://doi.org/10.1134/S0001434622030087}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128970893}
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  • https://doi.org/10.4213/mzm13255
  • https://www.mathnet.ru/eng/mzm/v111/i3/p403
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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