Classification of flag-transitive Steiner quadruple systems

2004/01/12 by Michael Huber · 1 citation
Mathematics · #math.CO #math.GR #msc:51E10 #msc:05B05 #msc:20B25

paper · pdf · doi:10.1006/jcta.2000.3141

published as Journal of Combinatorial Theory, Series A 94, 180-190 (2001) · 11 pages

arxiv created 2004/01/12 · arxiv updated 2009/12/01

Abstract

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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