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Abstract
We investigate weakly half-factorial sets in finite abelian groups, a concept introduced by J. Śliwa to study half-factorial sets. We fully characterize weakly half-factorial sets in a given group, and determine the maximum cardinality of such a set. This leads to several new results on half-factorial sets; in particular we solve a problem of W. Narkiewicz in some special cases. We also study the arithmetical consequences of weakly-half-factoriality in terms of factorization lengths in block monoids.
Received: 2005-05-12
Revised: 2005-11-15
Published Online: 2007-09-25
Published in Print: 2007-07-01
© Walter de Gruyter
