Abstract
Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steinert-designs (i.e. flag-transitive t-(v,k,1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially characterize all flag-transitive Steiner 2-designs. However, despite the finite simple group classification, for Steiner t-designs with parameters t > 2 such characterizations have remained challenging open problems for about 40 years (cf. [11, p. 147] and [12 p. 273], but presumably dating back to around 1965). The object of the present paper is to give a complete classification of all flag-transitive Steiner 4-designs. Our result relies on the classification of the finite doubly transitive permutation groups and is a continuation of the author's work [20, 21] on the classification of all flag-transitive Steiner 3-designs.
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2000 Mathematics Subject Classification. Primary 51E10 . Secondary 05B05 . 20B25
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Huber, M. The classification of flag-transitive Steiner 4-designs. J Algebr Comb 26, 183–207 (2007). https://doi.org/10.1007/s10801-006-0053-0
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DOI: https://doi.org/10.1007/s10801-006-0053-0