Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics)
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



PFMT:
Year:
Volume:
Issue:
Page:
Find






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


PFMT, 2017, Issue 4(33), Pages 76–83 (Mi pfmt539)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Separability of the lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups

V. G. Safonov, I. N. Safonova

Belarusian State University, Minsk

Abstract: Let $\mathfrak{X}$ be a non-empty class of finite groups. A complete lattice $\theta$ of formations is said to be $\mathfrak{X}$-separable if for every term $\nu(x_1,…, x_n)$ of signature $\{\cap,\lor_\theta\}$, $\theta$-formations $\mathfrak{F}_1,…,\mathfrak{F}_n$ and every group $A\in\mathfrak{X}\cap\nu(\mathfrak{F}_1,…,\mathfrak{F}_n)$ exists $\mathfrak{X}$-groups $A_1\in \mathfrak{F}_1,…, A_n\in\mathfrak{F}_n$, such that $A\in\nu(\theta\mathrm{form}A_1, …, \theta\mathrm{form}A_n)$. In particular, if $\mathfrak{X}=\mathfrak{G}$ is the class of all finite groups then the lattice $\theta$ of formations is said to be $\mathfrak{G}$-separable or, briefly, separable. It is proved that the lattice $l^\tau_{\omega_{\infty}}$ of all $\tau$-closed totally $\omega$-saturated formations is $\mathfrak{G}$-separable for any subgroup functor $\tau$.

Keywords: formation of finite groups, $\tau$-closed formation, totally $\omega$-saturated formation, lattice of formations, $\mathfrak{G}$-separated lattice of formations.

Full text: PDF file (396 kB)
References: PDF file   HTML file
UDC: 512.542
Received: 14.11.2017

Citation: V. G. Safonov, I. N. Safonova, “Separability of the lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups”, PFMT, 2017, no. 4(33), 76–83

Citation in format AMSBIB
\Bibitem{SafSaf17}
\by V.~G.~Safonov, I.~N.~Safonova
\paper Separability of the lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups
\jour PFMT
\yr 2017
\issue 4(33)
\pages 76--83
\mathnet{http://mi.mathnet.ru/pfmt539}


Linking options:
  • http://mi.mathnet.ru/eng/pfmt539
  • http://mi.mathnet.ru/eng/pfmt/y2017/i4/p76

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Shcherbina, “Algebraicity of lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups”, Ufa Math. J., 12:1 (2020), 82–90  mathnet  crossref  isi
    2. N. N. Vorobev, I. I. Staselko, A. O. Khodzhagulyev, “Otdelimye reshetki kratno $\sigma$-lokalnykh formatsii”, Sib. matem. zhurn., 62:4 (2021), 721–735  mathnet  crossref
  • Проблемы физики, математики и техники
    Number of views:
    This page:71
    Full text:19
    References:10

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021