On the Invariant Rings of Modular Bireflection Groups with Applications of Macaulay's Double Annihilator Correspondence

Let V be a faithful finite-dimensional representation of a finite group G over an odd prime field k, and S = k[V], the symmetric algebra on the dual V*. Chapter 2 shows how to find the invariant ring S^G when G is an abelian unipotent two-row group. The invariant rings are complete intersections.

Chapter 3 shows an algorithm that computes the Macaulay inverse for any homogenous (S^+)-primary irreducible ideal of S. It will also be shown that the Hilbert ideal of the invariant rings of the abelian two-row groups from chapter 2 are complete intersection ideals with inverse monomials as Macaulay inverses.