Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matematicheskie Zametki, 2022, Volume 112, Issue 6, Pages 839–849
DOI: https://doi.org/10.4213/mzm13553
(Mi mzm13553)
 

This article is cited in 1 scientific paper (total in 1 paper)

On Questions Posed by Shemetkov, Ballester-Bolinches, and Perez-Ramos in Finite Group Theory

V. I. Murashka

Gomel State University named after Francisk Skorina
Full-text PDF (495 kB) Citations (1)
References:
Abstract: A chief factor $H/K$ of a group $G$ is said to be $\mathfrak{F}$-central if $(H/K)\rtimes (G/C_G(H/K))\in\mathfrak{F}$. In 1997, Shemetkov posed the problem of describing finite group formations $\mathfrak{F}$ such that $\mathfrak{F}$ coincides with the class of groups for which all chief factors are $\mathfrak{F}$-central. We refer to such formations as centrally saturated. We prove that the centrally saturated formations form a complete distributive lattice. As an answer to a question posed by Ballester-Bolinches and Perez-Ramos, conditions for a centrally saturated formation to be saturated and solvably saturated in the class of all groups are found. As a consequence, a criterion for hereditary Fitting formations to be solvably saturated is obtained.
Keywords: finite group, saturated formation, solvably saturated formation, centrally saturated formation, $\mathfrak{F}$-hypercenter, distributive lattice.
Received: 18.04.2022
Revised: 20.07.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 6, Pages 932–939
DOI: https://doi.org/10.1134/S000143462211027X
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. I. Murashka, “On Questions Posed by Shemetkov, Ballester-Bolinches, and Perez-Ramos in Finite Group Theory”, Mat. Zametki, 112:6 (2022), 839–849; Math. Notes, 112:6 (2022), 932–939
Citation in format AMSBIB
\Bibitem{Mur22}
\by V.~I.~Murashka
\paper On Questions Posed by Shemetkov, Ballester-Bolinches, and Perez-Ramos in Finite Group Theory
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 6
\pages 839--849
\mathnet{http://mi.mathnet.ru/mzm13553}
\crossref{https://doi.org/10.4213/mzm13553}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4439554}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 6
\pages 932--939
\crossref{https://doi.org/10.1134/S000143462211027X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85166247180}
Linking options:
  • https://www.mathnet.ru/eng/mzm13553
  • https://doi.org/10.4213/mzm13553
  • https://www.mathnet.ru/eng/mzm/v112/i6/p839
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:196
    Full-text PDF :31
    References:54
    First page:6
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024