Invariants of the dihedral group $D_{2p}$ 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 integer 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. As well, we give an explicit description of a separating set when $p$ is prime.

7 pages

References in corpus (1)

• Degree bounds for separating invariants

Cited by in corpus (2)

• Zero-separating invariants for finite groups
• Gröbner bases for the Hilbert ideal and coinvariants of the Dihedral group $D_{2p}$}