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 group and G 0⊆ G be a subset. A sequence over G 0 means a finite sequence of
terms from G 0, where the order of elements is disregarded and the repetition of elements is …

Degree bounds for algebra generators of invariant rings are a topic of longstanding interest
in invariant theory. We study the analogous question for field generators for the field of …

Let G be a finite group and exp (G)= lcm {ord (g)∣ g∈ G}. A finite unordered sequence of
terms from G, where repetition is allowed, is a product-one sequence if its terms can be …

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 …

The computation of the Noether numbers of all groups of order less than thirty-two is
completed. It turns out that for these groups in non-modular characteristic the Noether …

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool
for the study of regular Cayley maps and, more generally, for finite groups with a …

It is proved that the universal degree bound for separating polynomial invariants of a finite
abelian group (in non-modular characteristic) is typically strictly smaller than the universal …

Let G be a finite group. A finite unordered sequence S= g 1∙⋯∙ g ℓ of terms from G, where
repetition is allowed, is a product-one sequence if its terms can be ordered such that their …

Let G be a finite group. A sequence over G means a finite sequence of terms from G, where
repetition is allowed and the order is disregarded. A product-one sequence is a sequence …