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On the separating Noether number of finite abelian groups
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abstract
The separating Noether number $\beta_{\mathrm{sep}}(G)$ of a finite group $G$ is the minimal positive integer $d$ such that for every finite $G$-module $V$ there is a separating set consisting of invariant polynomials of degree at most $d$. In this paper we use methods from additive combinatorics to investigate the separating Noether number for finite abelian groups. Among others, we obtain the exact value of $\beta_{\mathrm{sep}}(G)$, provided that $G$ is either a $p$-group or has rank $2$, $3$ or $5$.
Forward citations
Cited by 2 Pith papers
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Separating polynomial invariants over non-closed fields of finite abelian groups
Over Q, degree 3 polynomial invariants separate orbits of C_p representations; a new Galois-descent condition yields analogous degree bounds for abelian groups over non-closed fields.
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Generic orbits, normal bases, and generation degree for fields of rational invariants
Theorem: for faithful finite group actions in characteristic not dividing the group order, β_field ≤ 2D_span + 1, and equality is attained.
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