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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
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
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
Linking options:
https://www.mathnet.ru/eng/al133 https://www.mathnet.ru/eng/al/v44/i5/p601
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Abstract page: | 425 | Full-text PDF : | 124 | References: | 59 | First page: | 1 |
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