The property of being equationally Noetherian for some soluble groups |
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Authors: | Ch K Gupta N S Romanovskii |
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Institution: | (1) University of Manitoba, Winnipeg, Canada;(2) Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia |
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Abstract: | Let B be a class of groups A which are soluble, equationally Noetherian, and have a central series A = A1 ⩾ A2 ⩾ … An ⩾ … such that ⋂An = 1 and all factors An/An+1 are torsion-free groups; D is a direct product of finitely many cyclic groups of infinite or prime orders. We prove that
the wreath product D ≀ A is an equationally Noetherian group. As a consequence we show that free soluble groups of arbitrary
derived lengths and ranks are equationally Noetherian.
Supported by RFBR grant No. 05-01-00292.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 46–59, January–February, 2007. |
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Keywords: | equationally Noetherian group free soluble group |
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