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Algebra i logika, 2005, Volume 44, Number 5, Pages 601–621 (Mi al133)  

This article is cited in 13 scientific papers (total in 13 papers)

Irreducible Algebraic Sets in Metabelian Groups

V. N. Remeslennikov, N. S. Romanovskiia

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: We present the construction for a $u$-product $G_1\circ G_2$ of two $u$-groups $G_1$ and $G_2$, and prove that $G_1\circ G_2$ is also a $u$-group and that every $u$-group, which contains $G_1$ and $G_2$ as subgroups and is generated by these, is a homomorphic image of $G_1\circ G_2$. It is stated that if $G$ is a $u$-group then the coordinate group of an affine space $G^n$ is equal to $G \circ F_n$, where $F_n$ is a free metabelian group of rank $n$. Irreducible algebraic sets in $G$ are treated for the case where $G$ is a free metabelian group or wreath product of two free Abelian groups of finite ranks.
Keywords: $u$-group, $u$-product, coordinate group of an affine space, free metabelian group, free Abelian group.
Received: 23.02.2005
English version:
Algebra and Logic, 2005, Volume 44, Issue 5, Pages 336–347
DOI: https://doi.org/10.1007/s10469-005-0032
Bibliographic databases:
UDC: 512.5
Language: Russian
Citation: V. N. Remeslennikov, N. S. Romanovskii, “Irreducible Algebraic Sets in Metabelian Groups”, Algebra Logika, 44:5 (2005), 601–621; Algebra and Logic, 44:5 (2005), 336–347
Citation in format AMSBIB
\Bibitem{RemRom05}
\by V.~N.~Remeslennikov, N.~S.~Romanovskii
\paper Irreducible Algebraic Sets in Metabelian Groups
\jour Algebra Logika
\yr 2005
\vol 44
\issue 5
\pages 601--621
\mathnet{http://mi.mathnet.ru/al133}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2195022}
\zmath{https://zbmath.org/?q=an:1104.20028}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 5
\pages 336--347
\crossref{https://doi.org/10.1007/s10469-005-0032}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-27544473308}
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  • https://www.mathnet.ru/eng/al133
  • https://www.mathnet.ru/eng/al/v44/i5/p601
  • This publication is cited in the following 13 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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