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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Flag-transitive Steiner Designs (Paperback, 2009 ed.)
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Flag-transitive Steiner Designs (Paperback, 2009 ed.)
Series: Frontiers in Mathematics
Expected to ship within 10 - 15 working days
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The characterization of combinatorial or geometric structures in
terms of their groups of automorphisms has attracted considerable
interest in the last decades and is now commonly viewed as a
natural generalization of Felix Klein's Erlangen
program(1872).Inaddition,especiallyfor?nitestructures,importantapplications
to practical topics such as design theory, coding theory and
cryptography have made the ?eld even more attractive. The subject
matter of this research monograph is the study and class- cation of
?ag-transitive Steiner designs, that is, combinatorial t-(v,k,1)
designs which admit a group of automorphisms acting transitively on
incident point-block pairs. As a consequence of the classi?cation
of the ?nite simple groups, it has been possible in recent years to
characterize Steiner t-designs, mainly for t=2,adm- ting groups of
automorphisms with su?ciently strong symmetry properties. For
Steiner 2-designs, arguably the most general results have been the
classi?cation of all point 2-transitive Steiner 2-designs in 1985
by W. M. Kantor, and the almost complete determination of all
?ag-transitive Steiner 2-designs announced in 1990
byF.Buekenhout,A.Delandtsheer,J.Doyen,P.B.Kleidman,M.W.Liebeck, and
J. Saxl. However, despite the classi?cation of the ?nite simple
groups, for Steiner t-designs witht> 2 most of the
characterizations of these types have remained long-standing
challenging problems. Speci?cally, the determination of all ?-
transitive Steiner t-designs with 3? t? 6 has been of particular
interest and object of research for more than 40 years.
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