2-(v,k,3) designs admitting an almost simple, flag-transitive automorphism group with socle PSL(2,q)

TL;DR

This paper classifies all non-trivial 2-(v,k,3) combinatorial designs that have an automorphism group with a specific symmetry property related to PSL(2,q).

Contribution

It provides a complete classification of 2-(v,k,3) designs with an almost simple, flag-transitive automorphism group having socle PSL(2,q).

Findings

Complete classification of the specified designs.

Identification of conditions for existence of such designs.

Clarification of symmetry properties in these designs.

Abstract

In this paper, we completely classify the non-trivial 2-(v,k,3) designs admitting an almost simple, flag-transitive automorphism group with socle PSL(2,q).