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 …

We study a class of orbit recovery problems in which we observe independent copies of an
unknown element of R p, each linearly acted upon by a random element of some group …

We determine the minimal number of separating invariants for the invariant ring of a matrix
group G≤ GL n (F q) over the finite field F q. We show that this minimal number can be …

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 …

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This article studies separating invariants for the ring of multisymmetric polynomials in $ m $
sets of $ n $ variables over an arbitrary field $\mathbb {K} $. We prove that in order to obtain …

The separating Noether number of a finite group is the minimal positive integer $ d $ such
that for any finite dimensional complex linear representation of the group, any two dictinct …

Let G be a linear algebraic group over an algebraically closed field 𝕜 acting rationally on a
G-module V with its null-cone. Let δ (G, V) and σ (G, V) denote the minimal number d such …

For a finite-dimensional representation V of a group G over a field F, the degree of reductivity
δ (G, V) is the smallest degree d such that every nonzero fixed point v∈ VG∖{0} can be …

Assume a fixed point v∈ VG can be separated from zero by a homogeneous invariant f∈ 𝕜
[V] G of degree prd, where p> 0 is the characteristic of the ground field 𝕜 and p, d are …