1.Centre de Mathématiques Laurent Schwartz,UMR 7640 du CNRS,Palaiseau Cedex,France;2.Institut für Mathematik und Wissenschaftliches Rechnen,Karl-Franzens-Universit?t Graz,Graz,Austria
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. This work was supported by the Austrian Science Fund FWF (Project P16770-N12) and by the Austrian-French Program ``Amadeus 2003–2004'.