Semi-regular Relative Difference Sets with Large Forbidden Subgroups
| dc.creator | Feng, Tao | |
| dc.creator | Xiang, Qing | |
| dc.date | 2008-01-22 | |
| dc.date.accessioned | 2026-07-07T08:55:51Z | |
| dc.date.available | 2026-07-07T08:55:51Z | |
| dc.description | Motivated by a connection between semi-regular relative difference sets and mutually unbiased bases, we study relative difference sets with parameters $(m,n,m,m/n)$ in groups of non-prime-power orders. Let $p$ be an odd prime. We prove that there does not exist a $(2p,p,2p,2)$ relative difference set in any group of order $2p^2$, and an abelian $(4p,p,4p,4)$ relative difference set can only exist in the group $\Bbb{Z}_2^2\times \Bbb{Z}_3^2$. On the other hand, we construct a family of non-abelian relative difference sets with parameters $(4q,q,4q,4)$, where $q$ is an odd prime power greater than 9 and $q\equiv 1$ (mod 4). When $q=p$ is a prime, $p>9$, and $p\equiv$ 1 (mod 4), the $(4p,p,4p,4)$ non-abelian relative difference sets constructed here are genuinely non-abelian in the sense that there does not exist an abelian relative difference set with the same parameters. | |
| dc.identifier | https://arxiv.org/abs/0801.3394 | |
| dc.identifier | http://arxiv.org/abs/0801.3394 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146407 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B10 | |
| dc.title | Semi-regular Relative Difference Sets with Large Forbidden Subgroups | |
| dc.type | text |