Inverse zero-sum problems and algebraic invariants

Benjamin Girard (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

In this article, we study the maximal cross number of long zero-sumfree sequences in a finite Abelian group. Regarding this inverse-type problem, we formulate a general conjecture and prove, among other results, that this conjecture holds true for finite cyclic groups, finite Abelian p-groups and for finite Abelian groups of rank two. Also, the results obtained here enable us to improve, via the resolution of a linear integer program, a result of W. Gao and A. Geroldinger concerning the minimal number of elements with maximal order in a long zero-sumfree sequence of a finite Abelian group of rank two.

Mots clés: zero-sumfree sequence; cross number; Davenport constant; finite Abelian groups; linear integer program

Domaines: Théorie des nombres [math.NT]; Combinatoire [math.CO]; Théorie des groupes [math.GR]

Benjamin Girard. Inverse zero-sum problems and algebraic invariants. Acta Arithmetica, 2008, 135 (3), pp.231-246. ⟨10.4064/aa135-3-3⟩. ⟨hal-00289737v2⟩