Algebra i logika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






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


Algebra i logika, 2023, Volume 62, Number 1, Pages 102–113
DOI: https://doi.org/10.33048/alglog.2023.62.107
(Mi al2750)
 

Generic types and generic elements in divisible rigid groups

A. G. Myasnikova, N. S. Romanovskiib

a Charles V. Schaefer, Jr. School of Engineering & Science, Stevens Institute of Technology
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: A group $G$ is said to be $m$-rigid if it contains a normal series of the form
$$G=G_1>G_2>\ldots>G_m>G_{m+1}=1,$$
whose quotients $G_i/G_{i+1}$ are Abelian and, treated as (right) ${\mathbb{Z}}[G/G_i]$-modules, are torsion-free. A rigid group $G$ is said to be divisible if elements of the quotient $\rho_i(G)/\rho_{i+1}(G)$ are divisible by nonzero elements of the ring ${\mathbb{Z}}[G/\rho_i(G)]$. Previously, it was proved that the theory of divisible $m$-rigid groups is complete and $\omega$-stable. In the present paper, we give an algebraic description of elements and types that are generic over a divisible $m$-rigid group $G$.
Keywords: divisible $m$-rigid group, generic type, generic element.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0002
Received: 22.02.2022
Revised: 30.10.2023
Document Type: Article
UDC: 512.5:510.6
Language: Russian
Citation: A. G. Myasnikov, N. S. Romanovskii, “Generic types and generic elements in divisible rigid groups”, Algebra Logika, 62:1 (2023), 102–113
Citation in format AMSBIB
\Bibitem{MyaRom23}
\by A.~G.~Myasnikov, N.~S.~Romanovskii
\paper Generic types and generic elements in divisible rigid groups
\jour Algebra Logika
\yr 2023
\vol 62
\issue 1
\pages 102--113
\mathnet{http://mi.mathnet.ru/al2750}
\crossref{https://doi.org/10.33048/alglog.2023.62.107}
Linking options:
  • https://www.mathnet.ru/eng/al2750
  • https://www.mathnet.ru/eng/al/v62/i1/p102
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
    Statistics & downloads:
    Abstract page:54
    Full-text PDF :14
    References:7
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024