Almost simple groups of Lie type and symmetric designs with \(\lambda\) prime

In this article, we investigate symmetric \((v,k,\lambda)\) designs \(\mathcal{D}\) with \(\lambda\) prime admitting flag-transitive and point-primitive automorphism groups \(G\). We prove that if \(G\) is an almost simple group with socle a finite simple group of Lie type, then \(\mathcal{D}\) is e...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-09
Main Authors: Seyed Hassan Alavi, Bayat, Mohsen, Daneshkhah, Ashraf
Format: Article
Language:English
Subjects:
Automorphisms
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we investigate symmetric \((v,k,\lambda)\) designs \(\mathcal{D}\) with \(\lambda\) prime admitting flag-transitive and point-primitive automorphism groups \(G\). We prove that if \(G\) is an almost simple group with socle a finite simple group of Lie type, then \(\mathcal{D}\) is either the point-hyperplane design of a projective space \(\mathrm{PG}_{n-1}(q)\), or it is of parameters \((7,4,2)\), \((11,5,2)\), \((11,6,2)\) or \((45,12,3)\).
ISSN:2331-8422