Degree bound for separating invariants of abelian groups
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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.References
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Additional Information
- M. Domokos
- Affiliation: MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, 1053 Budapest, Hungary
- MR Author ID: 345568
- Email: domokos.matyas@renyi.mta.hu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3695-3708
- MSC (2010): Primary 13A50; Secondary 11B75, 20K01
- DOI: https://doi.org/10.1090/proc/13534
- MathSciNet review: 3665025