Flag-transitive automorphism groups of 2-designs with λ ≥ (r, λ)2 and an application to symmetric designs

Shenglin Zhou, Xiaoqin Zhan

Abstract


Let D be a 2-(v, k, λ) design with λ ≥ (r, λ)2. If G ≤ Aut(D) is flag-transitive, then G cannot be of simple diagonal or twisted wreath product type, and if G is product type then the socle of G has exactly two components and G has rank 3. Furthermore, we prove that if D is symmetric, then G must be an affine or almost simple group.

Keywords


2-design, automorphism group, primitivity, flag-transitivity.

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DOI: https://doi.org/10.26493/1855-3974.1165.105

ISSN: 1855-3974

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