Irreducible Algebraic Sets in Metabelian Groups |
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Authors: | V N Remeslennikov N S Romanovskii |
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Institution: | (1) Ordzhonikidze 13-202, Omsk, 644099, Russia;(2) Institute of Mathematics SB, RAS, Akademika Koptyuga Prospekt, 4, Novosibirsk, 630090, Russia |
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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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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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Keywords: | u-group u-product coordinate group of an affine space free metabelian group free Abelian group |
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