On symmetric 2-designs of prime order with almost simple flag-transitive automorphism groups

TL;DR

This paper classifies symmetric 2-designs of prime order that admit a flag-transitive automorphism group of almost simple type, completing the understanding of their structure and automorphism groups.

Contribution

It provides a complete classification of symmetric 2-designs of prime order with flag-transitive almost simple automorphism groups, extending previous results on their automorphism group types.

Findings

Automorphism group must be point-primitive

Automorphism group is of affine or almost simple type

Complete classification of designs with almost simple automorphism groups

Abstract

In this article, we investigate symmetric 2-designs of prime order admitting a flag-transitive automorphism group G. Recently, the authors proved that the automorphism group G of this type of designs must be point-primitive, and is of affine or almost simple type. Here, we give the complete classification of symmetric 2-designs of prime order, admitting a flag-transitive almost simple automorphism group.