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Sibirsk. Mat. Zh., 2018, Volume 59, Number 4, Pages 891–896 (Mi smj3017)  

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

Generalized rigid groups: definitions, basic properties, and problems

N. S. Romanovskiiab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We find a natural generalization of the concept of rigid group. The generalized rigid groups are also called $r$-groups. The terms of the corresponding rigid series of every $r$-group can be characterized by both $\exists$-formulas and $\forall$-formulas. We find a recursive system of axioms for the class of $r$-groups of fixed solubility length. We define divisible $r$-groups and give an appropriate system of axioms. Several fundamental problems are stated.

Keywords: soluble group, divisible group, group axioms.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
The author was supported by the Russian Science Foundation (Grant 14-21-00065).


DOI: https://doi.org/10.17377/smzh.2018.59.412

Full text: PDF file (270 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:4, 705–709

Bibliographic databases:

UDC: 512.5+510.6
Received: 16.11.2017

Citation: N. S. Romanovskii, “Generalized rigid groups: definitions, basic properties, and problems”, Sibirsk. Mat. Zh., 59:4 (2018), 891–896; Siberian Math. J., 59:4 (2018), 705–709

Citation in format AMSBIB
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\by N.~S.~Romanovskii
\paper Generalized rigid groups: definitions, basic properties, and problems
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 4
\pages 891--896
\mathnet{http://mi.mathnet.ru/smj3017}
\crossref{https://doi.org/10.17377/smzh.2018.59.412}
\elib{http://elibrary.ru/item.asp?id=35725950}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 4
\pages 705--709
\crossref{https://doi.org/10.1134/S0037446618040122}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000443717700012}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052996130}


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    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. N. S. Romanovskii, “Generalized rigid metabelian groups”, Siberian Math. J., 60:1 (2019), 148–152  mathnet  crossref  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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