This project is concerned with deriving certain invariants associated with the finite presentation of metabelian and solvable groups. These invariants have been shown to have many connections with number theory, algebraic geometry and topology. The invariants enable one to describe locally the property of having a finite Eilenberg.MacLane space up to a fixed dimension. In this proposal the principal investigator will study these invariants using equivariant homology. This approach will unify this theory as it appears in commutative algebra and in topology, as well as, provide a better understanding of the theory.
