Abstract
We present the construction for a u-product G1 ○ G2 of two u-groups G1 and G2, and prove that G1 ○ G2 is also a u-group and that every u-group, which contains G1 and G2 as subgroups and is generated by these, is a homomorphic image of G1 ○ G2. It is stated that if G is a u-group then the coordinate group of an affine space Gn is equal to G ○ Fn, where Fn 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.
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REFERENCES
G. Baumslag, A. Myasnikov, and V. Remeslennikov, “Algebraic geometry over groups,” J. Alg., 219, No.1, 16–79 (1999).
A. Myasnikov and V. Remeslennikov, “Algebraic geometry over groups. II. Logical foundations,” J. Alg., 234, No.1, 225–276 (2000).
V. N. Remeslennikov and N. S. Romanovskii, “Metabelian products of groups,” Algebra Logika, 43, No.3, 341–352 (2004).
V. Remeslennikov and R. Stohr, “On algebraic sets over metabelian groups,” to appear in J. Group Theory.
O. Chapuis, “∀-Free metabelian groups,” J. Symb. Log., 62, No.1, 159–174 (1997).
V. N. Remeslennikov and V. G. Sokolov, “Some properties of the Magnus embedding,” Algebra Logika, 9, No.5, 566–578 (1970).
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 601–621, September–October, 2005.
Supported by RFBR grant No. 05-01-00292, by FP “Universities of Russia” grant No. 04.01.053, and by RF Ministry of Education grant No. E00-1.0-12.
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Remeslennikov, V.N., Romanovskii, N.S. Irreducible Algebraic Sets in Metabelian Groups. Algebr Logic 44, 336–347 (2005). https://doi.org/10.1007/s10469-005-0032-x
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DOI: https://doi.org/10.1007/s10469-005-0032-x