BLOCK-TRANSITIVE 5 – (v, k, 2) DESIGNS AND SUZUKI GROUPS

Abstract

This article is a contribution to the study of the automorphism groups of 4 − (v, k, λ) designs. Let S = (P, B) be a non-trivial 4 − (q 2 + 1, k, 4) design, where q = 2 2n+1 for some positive integer n ≥ 1, and G ≤ Aut(S) acts block-transitively on S. If the socle of G is isomorphic to the simple groups of Lie type Sz(q), then G is not flag-transitive.

Nonexistence of $2-(v, k, 1)$ designs admitting automorphism groups with socle $E_8(q)$

“…Ding [8] considered 2 .v; k; 1/ designs admitting block-transitive automorphism groups in AGL.1; q/ and prove the existence of 2 .v; 6; 1/ designs which have block-transitive but not flag-transitive automorphism groups in AGL.1; q/ (see [7]). Dai and Zhao consider 2 .v; 13; 1/ designs with point-primitive block-transitive unsolvable group of automorphisms whose socle is S´.2 2nC1 / in [5]. Recently, there have been a number contributions to this classification (see [13,14]).…”