Block-transitive t-(k^2,k,\lam) designs and simple exceptional groups of Lie type

TL;DR

This paper proves that for block-transitive t-(k^2,k,lam) designs, the automorphism group's socle cannot be a finite simple exceptional Lie type group, narrowing the classification of such designs.

Contribution

It establishes a non-existence result for certain symmetric designs with automorphism groups of exceptional Lie type, advancing the understanding of symmetry in combinatorial designs.

Findings

Socle of automorphism group cannot be an exceptional Lie type group

Restricts possible automorphism groups for these designs

Contributes to classification of symmetric combinatorial designs

Abstract

Let G be an automorphism group of a nontrivial t-(k^2,k,\lambda) design. In this paper, we prove that if G is block-transitive, then the socle of G cannot be a finite simple exceptional group of Lie type.