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The classification of flag-transitive Steiner 3-designs

Combinatorics 2018-07-04 v1 Group Theory
Authors: Michael Huber
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Abstract

We solve the long-standing open problem of classifying all 3-(v,k,1) designs with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom. Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F. Buekenhout, Elsevier Science, Amsterdam, 1995, p. 273; but presumably dating back to 1965). Our result relies on the classification of the finite 2-transitive permutation groups.

Keywords

flag-transitive designs flag varieties automorphism groups

Cite

@article{arxiv.math/0401350,
  title  = {The classification of flag-transitive Steiner 3-designs},
  author = {Michael Huber},
  journal= {arXiv preprint arXiv:math/0401350},
  year   = {2018}
}

Comments

27 pages; to appear in the journal "Advances in Geometry"

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