Analysing flag-transitive point-imprimitive 2-designs

TL;DR

This paper develops methods to analyze flag-transitive point-imprimitive 2-designs, leading to a classification of such designs with small lambda values, enhancing understanding of their automorphisms and parameters.

Contribution

It introduces general analytical methods and completes the classification of flag-transitive, point-imprimitive 2-designs with lambda up to 4.

Findings

Complete classification of flag-transitive, point-imprimitive 2-designs with λ ≤ 4.

New restrictions on automorphisms and parameters of these designs.

Development of a toolkit for analyzing similar combinatorial designs.

Abstract

In this paper we develop several general methods for analysing flag-transitive point-imprimitive $2$-designs, which give restrictions on both the automorphisms and parameters of such designs. These constitute a tool-kit for analysing these designs and their groups. We apply these methods to complete the classification of flag-transitive, point-imprimitive $2$-$(v,k,\lambda)$ designs with $\lambda$ at most $4$.