2011
DOI: 10.5802/jtnb.784
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Abstract: Abstract. A subset S of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of S is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, p-groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general res… Show more

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Cited by 18 publications
(17 citation statements)
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“…(m i − 1), though both inequalities may fail (see [20, Propositions 5.1.4 and 5.1.8, pp. 341], or [44] for related results regarding the strong Davenport constant).…”
Section: Notation and Overviewmentioning
confidence: 99%
“…(m i − 1), though both inequalities may fail (see [20, Propositions 5.1.4 and 5.1.8, pp. 341], or [44] for related results regarding the strong Davenport constant).…”
Section: Notation and Overviewmentioning
confidence: 99%
“…with the latter inequality above following from the former combined with (47). Now additionally assume that our setpartition B is chosen, subject to…”
Section: Define a New Setpartition Amentioning
confidence: 99%
“…In general, D * (G) ≤ D(G) ≤ |G|, where D * (G) := 1+ r i=1 (m i − 1), though both inequalities may be strict (see [6, Propositions 5.1.4 and 5.1.8, pp. 341], or [19] for related results regarding the strong Davenport constant).…”
Section: Notation and Overviewmentioning
confidence: 99%