Finite linear spaces with flag-transitive groups
Journal of Combinatorial Theory Series A
2-Transitive and flag-transitive designs
Proceedings of the Marshall Hall conference on Coding theory, design theory, group theory
Finite geometries
The classification of finite linear spaces with flag-transitive automorphism groups of affine type
Journal of Combinatorial Theory Series A
Classification of flag-transitive Steiner quadruple systems
Journal of Combinatorial Theory Series A
On finite linear spaces with almost simple flag-transitive automorphism groups
Journal of Combinatorial Theory Series A
The classification of flag-transitive Steiner 4-designs
Journal of Algebraic Combinatorics: An International Journal
Mathematical Methods in Computer Science
Note: On the Cameron--Praeger conjecture
Journal of Combinatorial Theory Series A
Combinatorial Designs for Authentication and Secrecy Codes
Foundations and Trends in Communications and Information Theory
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As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t=2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t2 most of these characterizations have remained long-standing challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 3驴t驴6 is of particular interest and has been open for about 40 years (cf. Delandtsheer (Geom. Dedicata 41, p. 147, 1992 and Handbook of Incidence Geometry, Elsevier Science, Amsterdam, 1995, p. 273), but presumably dating back to 1965). The present paper continues the author's work (see Huber (J. Comb. Theory Ser. A 94, 180---190, 2001; Adv. Geom. 5, 195---221, 2005; J. Algebr. Comb., 2007, to appear)) of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.