Grobner bases for the Hilbert ideal and coinvariants of the dihedral group D-2p

We consider a finite dimensional representation of the dihedral group D-2p over a field of characteristic two where p is an odd integer and study the corresponding Hilbert ideal I-H. We show that I-H has a universal Grobner basis consisting of invariants and monomials only. We provide sharp bounds for the degree of an element in this basis and in a minimal generating set for I-H. We also compute the top degree of coinvariants when p is prime. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim