Bases for rings of coinvariants

H.E.A. Campbell, I.P. Hughes, R.J. Shank and D.L. Wehlau

November 1996

Abstract. We study the multiplicative structure of rings
of coinvariants for finite groups. We develop methods which
give rise to natural monomial bases for such rings over 
their ground fields and explicitly determine precisely which
monomials are zero in the ring of coinvariants. We apply
our methods to the Dickson, upper triangular and symmetric
coinvariants. Along the way, we recover theorems of Steinberg
[17] and E. Artin [1]. Using these monomial bases we prove
that the image of the transfer for a general linear group
over a finite field is a principal ideal in the ring of
invariants.