Let S be finite nonempty set of inequivlent valuations on Fp(t), and OS be the ring of S-integers. If Bn is the solvable, linear algebraic group of upper triangular matrices with determinant 1, then the solvable S-arithmetic group Bn(OS) has a finite index subgroup with infinite dimensional cohomology group in dimension |S|.

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...