Submission date: 12 December 2007. Revised version 26 May 2010.

Abstract:

We yield counterexamples to a Conjecture of Nesin, since we build a connected solvable group of finite Morley rank that no normal nilpotent subgroup has a nilpotent complement. On the other hand, our main result says that, each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T such that G is the semi-direct product of U by T, if and only if, for any field K of finite Morley rank, the connected definable subgroups of its multiplicative group are pseudo-tori.

Mathematics Subject Classification: 03C60, 20A15

Keywords and phrases: Maximal tori, Unipotent radical

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