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The critical number of finite abelian groups |
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| Authors: | Michael Freeze Weidong Gao |
| Affiliation: | a The University of North Carolina at Wilmington, Department of Mathematics and Statistics, Wilmington, NC 28403-5970, USA b Center for Combinatorics, Nankai University, Tianjin 300071, PR China c Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010 Graz, Austria |
| Abstract: | Let G be an additive, finite abelian group. The critical number cr(G) of G is the smallest positive integer ? such that for every subset S⊂G?{0} with |S|?? the following holds: Every element of G can be written as a nonempty sum of distinct elements from S. The critical number was first studied by P. Erd?s and H. Heilbronn in 1964, and due to the contributions of many authors the value of cr(G) is known for all finite abelian groups G except for G≅Z/pqZ where p,q are primes such that  . We determine that cr(G)=p+q−2 for such groups. |
| Keywords: | 11P70 11B50 11B75 |
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