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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 4, Pages 891–896
DOI: https://doi.org/10.17377/smzh.2018.59.412 (Mi smj3017) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Generalized rigid groups: definitions, basic properties, and problems

N. S. Romanovskiiab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (270 kB) Citations (5)
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DOI: https://doi.org/10.17377/smzh.2018.59.412
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).
Received: 16.11.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 4, Pages 705–709
DOI: https://doi.org/10.1134/S0037446618040122
Bibliographic databases:
Document Type: Article
UDC: 512.5+510.6
Language: Russian
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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