Zero-sumfree sequences in cyclic groups and some arithmetical application

Alfred Geroldinger; Yahya Ould Hamidoune

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 1, page 221-239
  • ISSN: 1246-7405

Abstract

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We show that in a cyclic group with n elements every zero-sumfree sequence S with length | S | ≥ n + 1 2 contains some element of order n with high multiplicity.

How to cite

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Geroldinger, Alfred, and Hamidoune, Yahya Ould. "Zero-sumfree sequences in cyclic groups and some arithmetical application." Journal de théorie des nombres de Bordeaux 14.1 (2002): 221-239. <http://eudml.org/doc/248919>.

@article{Geroldinger2002,
abstract = {We show that in a cyclic group with $n$ elements every zero-sumfree sequence $S$ with length $|S| \ge \frac\{n+1\}\{ 2\}$ contains some element of order $n$ with high multiplicity.},
author = {Geroldinger, Alfred, Hamidoune, Yahya Ould},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {zero-sum free sequences; cyclic groups; factorization in Krull monoids},
language = {eng},
number = {1},
pages = {221-239},
publisher = {Université Bordeaux I},
title = {Zero-sumfree sequences in cyclic groups and some arithmetical application},
url = {http://eudml.org/doc/248919},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Geroldinger, Alfred
AU - Hamidoune, Yahya Ould
TI - Zero-sumfree sequences in cyclic groups and some arithmetical application
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 1
SP - 221
EP - 239
AB - We show that in a cyclic group with $n$ elements every zero-sumfree sequence $S$ with length $|S| \ge \frac{n+1}{ 2}$ contains some element of order $n$ with high multiplicity.
LA - eng
KW - zero-sum free sequences; cyclic groups; factorization in Krull monoids
UR - http://eudml.org/doc/248919
ER -

References

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  2. [BEN75] J.D. Bovey, P. Erdös, I. Niven, Conditions for zero sum modulo n. Canad. Math. Bull.18 (1975), 27-29. Zbl0314.10040MR392901
  3. [CG97] S. Chapman, A. Geroldinger, Krull domains and monoids, their sets of lengths and associated combinatorial problems. In Factorization in integral domains, 73-112, Lecture Notes in Pure and Appl. Math.189, Marcel Dekker, New York, 1997. Zbl0897.13001MR1460769
  4. [EE72] R.B. Eggleton, P. Erdös, Two combinatorial problems in group theory. Acta Arith.21 (1972), 111-116. Zbl0248.20068MR304508
  5. [Ger87] A. Geroldinger, On non-unique factorizations into irreducible elements II. Number theory, Vol. II (Budapest, 1987), 723-757, Colloq. Math. Soc. János Bolyai51, North-Holland, Amsterdam, 1990. Zbl0703.11057MR1058242
  6. [Ger88] A. Geroldinger, Über nicht-eindeutige Zerlegungen in irreduzible Elemente. Math. Z.197 (1988), 505-529. Zbl0618.12002MR932683
  7. [GG98] W. Gao, A. Geroldinger, On the structure of zerofree sequences. Combinatorica18 (1998), 519-527. Zbl0968.11016MR1722257
  8. [GG99] W. Gao, A. Geroldinger, On long minimal zero sequences in finite abelian groups. Period. Math. Hungar.38 (1999), 179-211. Zbl0980.11014MR1756238
  9. [GG00] W. Gao, A. Geroldinger, Systems of sets of lengths II. Abh. Math. Sem. Univ. Hamburg70 (2000), 31-49. Zbl1036.11054MR1809532
  10. [MS55] L. Moser, P. Scherk, Distinct elements in a set of sums. Amer. Math. Monthly62 (1955), 46-47. MR1528921

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