Resumen de The property of being equationally Noetherian for some soluble groups

Ch. K. Gupta, N. S. Romanovskii

• 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.