Block-transitive t-designs I: point-imprimitive designs

✍ Scribed by Peter J. Cameron; Cheryl E. Praeger

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 690 KB
• Volume: 118
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90051-t

✦ Synopsis

Cameron, P.J. and C.E. Praeger, Block-transitive t-design I: point-imprimitive designs, Discrete Mathematics 118 (1993) 33-43.

We study block-transitive, point-imprimitive t-(v, k, A) designs for fixed t, v and k. A simple argument shows that we can assume that such a design admits a maximal imprimitive subgroup of S, Delandtsheer and Doyen bounded v in terms of k assuming that t >2; we obtain stronger bounds assuming that t 2 3 or that the design is flag-transitive. We also give a structure theorem for designs which attain the Delandtsheer-Doyen bound for all but a few small values of k, and show that for most values of k, there are exactly three such nonisomorphic designs.