A note on Pollard's Theorem
| dc.creator | Hamidoune, Y. O. | |
| dc.creator | Serra, O. | |
| dc.date | 2008-04-16 | |
| dc.date.accessioned | 2026-07-07T09:32:57Z | |
| dc.date.available | 2026-07-07T09:32:57Z | |
| dc.description | Let $A,B$ be nonempty subsets of a an abelian group $G$. Let $N_i(A,B)$ denote the set of elements of $G$ having $i$ distinct decompositions as a product of an element of $A$ and an element of $B$. We prove that $$ \sum _{1\le i \le t} |N_i (A,B)|\ge t(|A|+|B|- t-α+1+w)-w, $$ where $α$ is the largest size of a coset contained in $AB$ and $w=\min (α-1,1)$, with a strict inequality if $α\ge 3$ and $t\ge 2$, or if $α\ge 2$ and $t= 2$. This result is a local extension of results by Pollard and Green--Ruzsa and extends also for $t>2$ a recent result of Grynkiewicz, conjectured by Dicks--Ivanov (for non necessarily abelian groups) in connection to the famous Hanna Neumann problem in Group Theory. | |
| dc.identifier | https://arxiv.org/abs/0804.2593 | |
| dc.identifier | http://arxiv.org/abs/0804.2593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158963 | |
| dc.subject | Number Theory | |
| dc.subject | 11B60, 11B34, 20D60 | |
| dc.title | A note on Pollard's Theorem | |
| dc.type | text |