1 Splitting in solvable groups of finite Morley rank

Abstract: We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The 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 = U o T, if and only if, for any field K of finite Morley rank, the connected definable subgroups of K ∗ are pseudo-tori. Also we build a centerless connected solvable group G of finite Morley rank with no definable representation over a direct sum of interpretable fields