Inverse zero-sum problems in finite Abelian p-groups

• Autorzy: Benjamin Girard
• Języki publikacji: EN

Abstrakty

EN

We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over G contains at least exp(G) - 1 elements of order exp(G), which improves a previous result of W. Gao and A. Geroldinger.

Kategorie tematyczne

• 20D60: Arithmetic and combinatorial problems
• 11B75: Other combinatorial number theory
• 11P70: Inverse problems of additive number theory, including sumsets
• 13F05: Dedekind, Pr\"ufer, Krull and Mori rings and their generalizations
• 11R27: Units and factorization
• 05E99: None of the above, but in this section
• 20K01: Finite abelian groups [For sumsets, see and ]

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 120
• Numer: 1
• Strony: 7-21

Daty

wydano

2010

Twórcy

autor

Benjamin Girard

• Centre de Mathématiques Laurent Schwartz, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau Cedex, France

Identyfikatory

DOI

10.4064/cm120-1-2