Hyper-atoms and the critical pair Theory
| dc.creator | Hamidoune, Yahya Ould | |
| dc.date | 2008-05-22 | |
| dc.date.accessioned | 2026-07-07T09:40:26Z | |
| dc.date.available | 2026-07-07T09:40:26Z | |
| dc.description | We introduce the notion of a hyper-atom. One of the main results of this paper is the $\frac{2|G|}3$--Theorem: Let $S$ be a finite generating subset of an abelian group $G$ of order $\ge 2$. Let $T$ be a finite subset of $G$ such that $2\le |S|\le |T|$, $S+T$ is aperiodic, $0\in S\cap T$ and $$ \frac{2|G|+2}3\ge |S+T|= |S|+|T|-1.$$ Let $H$ be a hyper-atom of $S$. Then $S$ and $T$ are $H$--quasi-periodic. Moreover $ϕ(S)$ and $ϕ(T)$ are arithmetic progressions with the same difference, where $ϕ:G\mapsto G/H$ denotes the canonical morphism. This result implies easily the traditional critical pair Theory and its basic stone: Kemperman's Structure Theorem. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0805.3522 | |
| dc.identifier | http://arxiv.org/abs/0805.3522 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161484 | |
| dc.subject | Number Theory | |
| dc.subject | 11B60; 11B34; 20D60 | |
| dc.title | Hyper-atoms and the critical pair Theory | |
| dc.type | text |