# Inverse zero-sum problems in finite Abelian p-groups

Colloquium Mathematicae (2010)

- Volume: 120, Issue: 1, page 7-21
- ISSN: 0010-1354

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topBenjamin Girard. "Inverse zero-sum problems in finite Abelian p-groups." Colloquium Mathematicae 120.1 (2010): 7-21. <http://eudml.org/doc/286600>.

@article{BenjaminGirard2010,

abstract = {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.},

author = {Benjamin Girard},

journal = {Colloquium Mathematicae},

keywords = {zero-sum; zero-sumfree sequence; abelian -group},

language = {eng},

number = {1},

pages = {7-21},

title = {Inverse zero-sum problems in finite Abelian p-groups},

url = {http://eudml.org/doc/286600},

volume = {120},

year = {2010},

}

TY - JOUR

AU - Benjamin Girard

TI - Inverse zero-sum problems in finite Abelian p-groups

JO - Colloquium Mathematicae

PY - 2010

VL - 120

IS - 1

SP - 7

EP - 21

AB - 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.

LA - eng

KW - zero-sum; zero-sumfree sequence; abelian -group

UR - http://eudml.org/doc/286600

ER -

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