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We consider a finite dimensional representation of the dihedral group  D  2 p   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 Gröbner 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.

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