The critical number of finite abelian groups
| dc.creator | Freeze, Michael | |
| dc.creator | Gao, Weidong | |
| dc.creator | Geroldinger, Alfred | |
| dc.date | 2008-10-17 | |
| dc.date.accessioned | 2026-07-07T10:11:17Z | |
| dc.date.available | 2026-07-07T10:11:17Z | |
| dc.description | Let G be an additive, finite abelian group. The critical number $\mathsf{cr}(G)$ of $G$ is the smallest positive integer $\ell$ such that for every subset $S \subset G \setminus \{0\}$ with $|S| \ge \ell$ 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. Erdős and H. Heilbronn in 1964, and due to the contributions of many authors the value of $\mathsf {cr}(G)$ is known for all finite abelian groups $G$ except for $G \cong \mathbb{Z}/pq\mathbb{Z}$ where $p,q$ are primes such that $p+\lfloor2\sqrt{p-2}\rfloor+1<q<2p$. We determine that $\mathsf {cr}(G)=p+q-2$ for such groups. | |
| dc.identifier | https://arxiv.org/abs/0810.3223 | |
| dc.identifier | http://arxiv.org/abs/0810.3223 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171818 | |
| dc.subject | Number Theory | |
| dc.subject | 11P70; 11B50; 11B75 | |
| dc.title | The critical number of finite abelian groups | |
| dc.type | text |