NDLI: The classification of flag-transitive Steiner 4-designs

Content Provider	Springer Nature Link
Author	Huber, Michael
Copyright Year	2006
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.
Starting Page	183
Ending Page	207
Page Count	25
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	26
Issue Number	2
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2007-01-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Steiner designs Flag-transitive group of automorphisms 2-transitive permutation group Group Theory and Generalizations Computer Science Order, Lattices, Ordered Algebraic Structures Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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