A DEGREE FORMULA FOR EQUIVARIANT COHOMOLOGY.

The primary theorem of this paper concerns the Poincaré (Hilbert) series for the cohomology ring of a finite group G with coefficients in a prime field of characteristic p. This theorem is proved using the ideas of equivariant cohomology whereby one considers more generally the cohomology ring of the Borel construction H*(EG ×G X), where X is a manifold on which G acts. This work results in a formula that computes the "degree" of the Poincaré series in terms of corresponding degrees of certain subgroups of the group G. In this paper, we discuss the theorem and the method of proof. [ABSTRACT FROM AUTHOR]