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Algebra i logika, 2020, Volume 59, Number 1, Pages 116–122
DOI: https://doi.org/10.33048/alglog.2020.59.107 (Mi al938) 		 
Metabelian pro-$p$-groups with a single relation

N. S. Romanovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/alglog.2020.59.107
Abstract: It is proved that there exist uncountably many nonisomorphic pro-$p$-groups admitting presentations with two generating elements and one defining relation in the variety of metabelian pro-$p$-groups.
Also we give information on pro-$p$-groups with a single relation in varieties of nilpotent pro-$p$-groups.
Keywords: pro-$p$-group, variety of metabelian pro-$p$-groups, variety of nilpotent pro-$p$-groups.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.1, проект 0314-2019-0001
Supported by SB RAS Fundamental Research Program I.1.1, project No. 0314-2019-0001.
Received: 29.01.2020
Revised: 30.04.2020
English version:
Algebra and Logic, 2020, Volume 59, Issue 1, Pages 82–86
DOI: https://doi.org/10.1007/s10469-020-09580-1
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: Russian
Citation: N. S. Romanovskii, “Metabelian pro-$p$-groups with a single relation”, Algebra Logika, 59:1 (2020), 116–122; Algebra and Logic, 59:1 (2020), 82–86
Citation in format AMSBIB
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\by N.~S.~Romanovskii
\paper Metabelian pro-$p$-groups with a single relation
\jour Algebra Logika
\yr 2020
\vol 59
\issue 1
\pages 116--122
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\crossref{https://doi.org/10.33048/alglog.2020.59.107}
\transl
\jour Algebra and Logic
\yr 2020
\vol 59
\issue 1
\pages 82--86
\crossref{https://doi.org/10.1007/s10469-020-09580-1}
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    		Алгебра и логика Algebra and Logic
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