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Degree bound for separating invariants of abelian groups


Author: M. Domokos
Journal: Proc. Amer. Math. Soc. 145 (2017), 3695-3708
MSC (2010): Primary 13A50; Secondary 11B75, 20K01
DOI: https://doi.org/10.1090/proc/13534
Published electronically: April 12, 2017
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Abstract: 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 degree bound for generators of polynomial invariants. More precisely, these degree bounds can be equal only if the group is cyclic or is the direct sum of $ r$ even order cyclic groups where the number of two-element direct summands is not less than the integer part of the half of $ r$. A characterization of separating sets of monomials is given in terms of zero-sum sequences over abelian groups.


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Additional Information

M. Domokos
Affiliation: MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, 1053 Budapest, Hungary
Email: domokos.matyas@renyi.mta.hu

DOI: https://doi.org/10.1090/proc/13534
Keywords: Separating invariants, zero-sum sequences, Noether number, Davenport constant
Received by editor(s): March 22, 2016
Received by editor(s) in revised form: October 5, 2016
Published electronically: April 12, 2017
Additional Notes: This research was partially supported by National Research, Development and Innovation Office, NKFIH K 119934.
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2017 American Mathematical Society

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