Barna Schefler

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20232025

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math.AC2025

Separating versus ordinary Noether numbers

Mátyás Domokos, Barna Schefler

Let $G$ be a finite group and $K$ a field containing an element of multiplicative order $∣ G ∣$ . It is shown that if $G$ has a cyclic subgroup of index at most $2$ , then the separati…

math.AC2025

On separating sets of polynomial invariants of finite abelian group actions

Barna Schefler, Kevin Zhao, Qinghai Zhong

Let $G$ be a finite group acting on a finite dimensional complex vector space $V$ via linear transformations. Let $C [V]^{G}$ be the algebra of polynomials that are invariant…

math.AC2025

On the separating Noether number of finite abelian groups

Barna Schefler, Kevin Zhao, Qinghai Zhong

The separating Noether number $β_{sep} (G)$ of a finite group $G$ is the minimal positive integer $d$ such that for every finite $G$ -module $V$ there is a separating set co…

math.AC2024

The separating Noether number of small groups

M. Domokos, B. Schefler

The present paper completes the computation of the separating Noether numbers for the groups with order strictly less than $32$ . Most of the results are proved for the case of a ge…

math.AC2024

The separating Noether number of abelian groups of rank two

Barna Schefler

The exact value of the separating Noether number of an arbitrary finite abelian group of rank two is determined. This is done by a detailed study of the monoid of zero-sum sequence…

math.AC2023

The separating Noether number of the direct sum of several copies of a cyclic group

Barna Schefler

The exact value of the separating Noether number of some finite abelian groups is determined, including the direct sums of cyclic groups of the same order.