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 results, establishing new lower bounds for the cardinality of zero-sumfree sets for various types of groups. The quality of these bounds is explored via the treatment, which is computer-aided, of selected explicit examples. Moreover, we investigate a closely related notion, namely the maximal cardinality of minimal zero-sum sets, i.e., the Strong Davenport constant. In particular, we determine its value for elementary p-groups of rank at most 2, paralleling and building on recent results on this problem for the Olson constant.
11It remains unclear if Phe was limiting in the Control ration or if RP Phe was not fed at high enough levels to have a measurable response on production. However, it is clear that AA limitations, requirements and production responses are governed by much more than plasma AA levels. Results further suggest that AA are bioactive metabolites to the extent that they can change animal performance, even when they are not "limiting" per se, and that their supplementation to practical dairy cattle diets should be approached with extreme caution for this reason.
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