Vol. 1, No. 2, 2008

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Invariant polynomials and minimal zero sequences

Bryson W. Finklea, Terri Moore, Vadim Ponomarenko and Zachary J. Turner

Vol. 1 (2008), No. 2, 159–165

A connection is developed between polynomials invariant under abelian permutation of their variables and minimal zero sequences in a finite abelian group. This connection is exploited to count the number of minimal invariant polynomials for various abelian groups.

invariant polynomials, minimal zero sequences, finite abelian group, block monoid, zero-sum
Mathematical Subject Classification 2000
Primary: 13A50, 20K01
Secondary: 20M14
Received: 28 October 2007
Accepted: 1 November 2007
Published: 1 July 2008

Communicated by Scott Chapman
Bryson W. Finklea
Terri Moore
Department of Mathematics
University of Nebraska-Lincoln
203 Avery Hall
Lincoln, NE 68588-0130
United States
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182
United States
Zachary J. Turner