This paper surveys and develops links between polynomial invariants of finite groups,
factorization theory of Krull domains, and product-one sequences over finite groups. The …

Let G be a multiplicative finite group and S= a 1⋅…⋅ aka sequence over G. We call S a
product-one sequence if 1=∏ i= 1 ka τ (i) holds for some permutation τ of {1,…, k}. The small …

We show that when a group acts on a polynomial ring over a field the ring of invariants has
Castelnuovo-Mumford regularity at most zero. As a consequence, we prove a well-known …

The finite groups having an indecomposable polynomial invariant of degree at least half the
order of the group are classified. It turns out that–apart from four sporadic exceptions–these …

If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions
on V is called separating if the following holds: If two elements v, v'from V can be separated …

We study semisimple Hopf algebra actions on Artin–Schelter regular algebras and prove
several upper bounds on the degrees of the minimal generators of the invariant subring, and …

Let V be an n-dimensional algebraic representation over an algebraically closed field K of a
group G. For m> 0, we study the invariant rings K [V m] G for the diagonal action of G on V m …

It is proven that for any representation over a field of characteristic 0 0 of the non-abelian
semidirect product of a cyclic group of prime order pp and the group of order 3 3 the …

Let 𝑉 be a complex representation of a finite group 𝐺 of order 𝑔. Derksen conjectured that
the 𝑝th syzygies of the invariant ring Sym (𝑉) 𝐺 are generated in degrees≤(𝑝+ 1) 𝑔. We …

The Hilbert ideal is the ideal generated by positive degree invariant polynomials of a finite
group. For a cyclic group of prime order p, we show that the image of the transfer lie in the …