Classification of flag-transitive Steiner quadruple systems

Details Classification of flag-transitive Steiner quadruple systems Classification of flag-transitive Steiner quadruple systems

2004-01-12

arxiv.org/abs/math/0401117v1

Journal of Combinatorial Theory, Series A 94, 180-190 (2001)

Mathematics

Combinatorics

11 pages

Scientific paper

10.1006/jcta.2000.3141

A Steiner quadruple system of order v is a 3-(v,4,1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the "still open and longstanding problem of classifying all flag-transitive 3-(v,k,1) designs" for the smallest value of k. Moreover, a generalization of a result of H. Lueneburg (1965, Math. Z. 89, 82-90) is achieved.

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