Sums of sets of abelian group elements

Text For a positive integer k, let f ( k ) denote the largest integer t such that for every finite abelian group G and every zero-sum free subset S of G, if | S | = k then | Σ ( S ) | ≥ t . In this paper, we prove that f ( k ) ≥ 1 6 k 2 , which significantly improves a result of J.E. Olson. We also supply some interesting results on f ( k ) . Video For a video summary of this paper, please visit https://youtu.be/ZEHZFRUVJKY .