Invariants of the dihedral group D2p in characteristic two

Abstract

We consider finite dimensional representations of the dihedral group D 2p over an algebraically closed field of characteristic two where p is an odd prime and study the degrees of generating and separating polynomials in the corresponding ring of invariants. We give an upper bound for the degrees of the polynomials in a minimal generating set that does not depend on p when the dimension of the representation is sufficiently large. We also show that p + 1 is the minimal number such that the invariants up to that degree always form a separating set. We also give an explicit description of a separating set. © Copyright Cambridge Philosophical Society 2011.