Mathematics of the USSR-Izvestiya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Mathematics of the USSR-Izvestiya, 1989, Volume 33, Issue 1, Pages 201–207
DOI: https://doi.org/10.1070/IM1989v033n01ABEH000821
(Mi im1208)
 

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

On filters in the lattice of quasivarieties of groups

A. I. Budkin
References:
Abstract: Suppose $\mathfrak M$ is a quasivariety of groups. Assume there exist finitely presented groups $A$ and $B$ such that $A\notin\mathfrak M$, $B\in\mathfrak M$, and $B$ is not contained in the quasivariety generated by $A$. It is proved that the principal filter generated in the lattice of quasivarieties of groups by has the cardinality of the continuum. In particular, the principal filters generated by a) the quasivariety generated by all proper varieties of groups, b) the quasivariety of all $RN$-groups and c) the quasivariety generated by all periodic groups, have the cardinality of the continuum. It is shown that the smallest quasivariety of groups containing all proper quasivarieties of groups in which nontrivial quasi-identities of the form
$$ (\forall\,x_1)\dots(\forall\,x_n)(f(x_1,\dots,x_n)=1\to g(x_1,\dots,x_n)=1), $$
are true, where $f$ and $g$ are terms of group signature, does not coincide with the class of all groups.
Bibliography: 12 titles.
Received: 26.11.1986
Bibliographic databases:
UDC: 512.543
MSC: 20E10
Language: English
Original paper language: Russian
Citation: A. I. Budkin, “On filters in the lattice of quasivarieties of groups”, Math. USSR-Izv., 33:1 (1989), 201–207
Citation in format AMSBIB
\Bibitem{Bud88}
\by A.~I.~Budkin
\paper On~filters in the lattice of quasivarieties of groups
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 201--207
\mathnet{http://mi.mathnet.ru//eng/im1208}
\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000821}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=966988}
\zmath{https://zbmath.org/?q=an:0668.20024|0656.20032}
Linking options:
  • https://www.mathnet.ru/eng/im1208
  • https://doi.org/10.1070/IM1989v033n01ABEH000821
  • https://www.mathnet.ru/eng/im/v52/i4/p875
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024