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Algebra i logika, 2020, Volume 59, Number 3, Pages 344–366
DOI: https://doi.org/10.33048/alglog.2020.59.305
(Mi al2619)
 

This article is cited in 7 scientific papers (total in 7 papers)

Divisible rigid groups. IV. Definable subgroups

N. S. Romanovskiiab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (260 kB) Citations (7)
References:
Abstract: A group $G$ is said to be rigid if it contains a normal series
$$G=G_1>G_2>\ldots>G_m>G_{m+1}=1,$$
whose quotients $G_i/G_{i+1}$ are Abelian and, when treated as right $\mathbb{Z} [G/G_i]$-modules, are torsion-free. A rigid group $G$ is divisible if elements of the quotient $G_i/G_{i+1}$ are divisible by nonzero elements of the ring $\mathbb{Z} [G/G_i]$. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters.
Keywords: rigid group, divisible group, definable subgroup.
Funding agency Grant number
Russian Science Foundation 19-11-00039
N. S. Romanovskii is supported by Russian Science Foundation, project No. 19-11-00039.
Received: 08.10.2019
Revised: 21.10.2020
English version:
Algebra and Logic, 2020, Volume 59, Issue 3, Pages 237–252
DOI: https://doi.org/10.1007/s10469-020-09596-7
Bibliographic databases:
Document Type: Article
UDC: 512.5:510.6
Language: Russian
Citation: N. S. Romanovskii, “Divisible rigid groups. IV. Definable subgroups”, Algebra Logika, 59:3 (2020), 344–366; Algebra and Logic, 59:3 (2020), 237–252
Citation in format AMSBIB
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\by N.~S.~Romanovskii
\paper Divisible rigid groups. IV. Definable subgroups
\jour Algebra Logika
\yr 2020
\vol 59
\issue 3
\pages 344--366
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\crossref{https://doi.org/10.33048/alglog.2020.59.305}
\transl
\jour Algebra and Logic
\yr 2020
\vol 59
\issue 3
\pages 237--252
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  • https://www.mathnet.ru/eng/al2619
  • https://www.mathnet.ru/eng/al/v59/i3/p344
    Cycle of papers
    This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Abstract page:180
    Full-text PDF :17
    References:24
    First page:6
     
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