Block-transitive 3-(v,k,1) designs on exceptional groups of Lie type

2023/05/14 by Ting Lan, Weijun Liu, Lan, Ting +3 · 2 citations
Mathematics · Engineering · Computer Science · #Finite Group Theory Research #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2305.08052

Abstract

Let D be a non-trivial G-block-transitive 3-(v,k,1) design, where T≤ G ≤ Aut(T) for some finite non-abelian simple group T. It is proved that if T is a simple exceptional group of Lie type, then T is either the Suzuki group ²B₂(q) or G₂(q). Furthermore, if T=²B₂(q) then the design D has parameters v=q²+1 and k=q+1, and so D is an inverse plane of order q; and if T=G₂(q) then the point stabilizer in T is either SL₃(q).2 or SU₃(q).2, and the parameter k satisfies very restricted conditions.

Cited by

• Block-transitive t-(k²,k,\lam) designs and simple exceptional groups of Lie type
• Large maximal subgroups of almost simple classical groups

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