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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 1, Pages 194–200
DOI: https://doi.org/10.33048/smzh.2019.60.116 (Mi smj3069) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Generalized rigid metabelian groups

N. S. Romanovskiiab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (273 kB) Citations (4)
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DOI: https://doi.org/10.33048/smzh.2019.60.116
Abstract: We study the generalized rigid groups ($r$-groups), in the metabelian case in more detail. The periodic $r$-groups are described. We prove that each divisible metabelian $r$-group decomposes as a semidirect product of two abelian subgroups, each metabelian $r$-group independently embeds into a divisible metabelian $r$-group, and the intersection of each collection of divisible subgroups of a metabelian $r$-group is divisible too.
Keywords: soluble group, metabelian group, divisible group.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00100_а
The author was supported by the Russian Foundation for Basic Research (Grant 18-01-00100).
Received: 09.03.2018
Revised: 09.03.2018
Accepted: 23.05.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 1, Pages 148–152
DOI: https://doi.org/10.1134/S0037446619010166
Bibliographic databases:
Document Type: Article
UDC: 512.5
MSC: 35R30
Language: Russian
Citation: N. S. Romanovskii, “Generalized rigid metabelian groups”, Sibirsk. Mat. Zh., 60:1 (2019), 194–200; Siberian Math. J., 60:1 (2019), 148–152
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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