Constructing subsets of a given packing index in Abelian groups
| dc.creator | Lyaskovska, N. | |
| dc.date | 2009-01-08 | |
| dc.date.accessioned | 2026-07-07T12:27:57Z | |
| dc.date.available | 2026-07-07T12:27:57Z | |
| dc.description | By definition, the sharp packing index $\ind_P^\sharp(A)$ of a subset $A$ of an abelian group $G$ is the smallest cardinal $κ$ such that for any subset $B\subset G$ of size $|B|\geκ$ the family $\{b+A:b\in B\}$ is not disjoint. We prove that an infinite Abelian group $G$ contains a subset $A$ with given index $\ind_P^\sharp(A)=κ$ if and only if one of the following conditions holds: (1) $2\le κ\le|G|^+$ and $k\notin \{3,4\}$; (2) $κ=3$ and $G$ is not isomorphic to $\oplus_{i\in I} \mathbb{Z}_3$; (3) $κ=4$ and $G$ is not isomorphic to $\oplus_{i\in I} \mathbb{Z}_2$ or to $\mathbb{Z}_4\oplus(\oplus_{i\in I} \mathbb{Z}_2)$. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0901.1151 | |
| dc.identifier | http://arxiv.org/abs/0901.1151 | |
| dc.identifier | Acta Univ. Carolinae, Math. Phys. 48:2 (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215387 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20K99, 05D05 | |
| dc.title | Constructing subsets of a given packing index in Abelian groups | |
| dc.type | text |