The K-theory of the title is described in terms of the Ktheory of finite subgroups, as generalized sheaf homology of a quotient space. A corollary is that if G is torsion-free, then the Whitehead groups Wh t(ZG) vanish for all i. 1. The main result. Suppose that G is a poly-(finite or cyclic) group. Then there is a virtually connected and solvable Lie group L that contains G as a discrete cocom...

According to Skolem’s conjecture, if an exponential Diophantine equation is not solvable, then it solvable modulo appropriately chosen modulus. Besides several concrete equations, the conjecture has only been proved for rather special cases. In

We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras.

The present article discusses the connection between exactly-solvable Schrödinger equations and the Liouville transformation. This transformation yields a large class of exactly-solvable potentials, which includes the relatively recently introduced potentials of Natanzon and Ginocchio. As well, this class is shown to contain two new families of exactly solvable potentials. AMS classification sc...

In this paper, all semigroups are assumed to be finite unless otherwise stated. If H is a pseudovariety of groups (that is, a class of groups closed under formation of finite direct products, subgroups and quotients groups), then it is natural to define a group to be Hsolvable if it has a subnormal series each of whose quotients belongs to H. For instance a group is solvable in the classical se...