The Noether number of the non-abelian group of order $$3p$$ 3 p

Abstract

It is proven that for any representation over a field of characteristic $$0$$ of the non-abelian semidirect product of a cyclic group of prime order $$p$$ and the group of order $$3$$ the corresponding algebra of polynomial invariants is generated by elements of degree at most $$p+2$$ . We also determine the exact universal degree bound for separating systems of polynomial invariants of this group in characteristic not dividing $$3p$$ .