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Matematicheskie Zametki, 2020, Volume 108, Issue 2, Pages 215–223
DOI: https://doi.org/10.4213/mzm12595
(Mi mzm12595)
 

This article is cited in 3 scientific papers (total in 3 papers)

Finite Groups with $\mathfrak F$-Subnormal Subgroups

M. N. Konovalova

Russian Academy of National Economy and Public Administration under the President of the Russian Federation (Bryansk Branch)
Full-text PDF (438 kB) Citations (3)
References:
Abstract: Let $G$ be a finite group, let $M$ be a maximal subgroup of $G$, and let $\mathfrak F$ be a hereditary formation consisting of solvable groups. The metanilpotency of the $\mathfrak F$-residual $G^\mathfrak F$ is established under the assumption that all subgroups maximal in $M$ are $\mathfrak F$-subnormal in $G$, and the nilpotency of $G^\mathfrak F$ is established in the case where $\mathfrak F$ is saturated. Properties of the group $G$ are indicated in more detail for the formation of all solvable groups with Abelian Sylow subgroups, for the formation of all supersolvable groups, and for the formation of all groups with nilpotent commutator subgroup.
Keywords: finite group, maximal subgroup, subnormal subgroup, formation, residual.
Received: 23.10.2019
English version:
Mathematical Notes, 2020, Volume 108, Issue 2, Pages 201–208
DOI: https://doi.org/10.1134/S0001434620070214
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: M. N. Konovalova, “Finite Groups with $\mathfrak F$-Subnormal Subgroups”, Mat. Zametki, 108:2 (2020), 215–223; Math. Notes, 108:2 (2020), 201–208
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v108/i2/p215
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    Full-text PDF :24
    References:26
    First page:3
     
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