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Mathematische Annalen

, Volume 333, Issue 4, pp 759–785 | Cite as

On the maximal cardinality of half-factorial sets in cyclic groups

  • Alain PlagneEmail author
  • Wolfgang A. Schmid
Article

Abstract

We consider the function μ(G), introduced by W. Narkiewicz, which associates to an abelian group G the maximal cardinality of a half-factorial subset of it. In this article, we start a systematic study of this function in the case where G is a finite cyclic group and prove several results on its behaviour. In particular, we show that the order of magnitude of this function on cyclic groups is the same as the one of the number of divisors of its cardinality.

Mathematics Subject Classification (2000)

11R27 11B75 11P99 20D60 20K01 05E99 13F05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Centre de Mathématiques Laurent SchwartzUMR 7640 du CNRSPalaiseau CedexFrance
  2. 2.Institut für Mathematik und Wissenschaftliches RechnenKarl-Franzens-Universität GrazGrazAustria

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