TY - JOUR

T1 - Block-transitive t-designs I

T2 - point-imprimitive designs

AU - Cameron, Peter J.

AU - Praeger, Cheryl E.

PY - 1993/8/1

Y1 - 1993/8/1

N2 - We study block-transitive, point-imprimitive t-(v,k,λ) 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 Sv. Delandtsheer and Doyen bounded v in terms of k assuming that t≥2; we obtain stronger bounds assuming that t≥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.

AB - We study block-transitive, point-imprimitive t-(v,k,λ) 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 Sv. Delandtsheer and Doyen bounded v in terms of k assuming that t≥2; we obtain stronger bounds assuming that t≥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.

UR - http://www.scopus.com/inward/record.url?scp=38249000725&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(93)90051-T

DO - 10.1016/0012-365X(93)90051-T

M3 - Article

AN - SCOPUS:38249000725

SN - 0012-365X

VL - 118

SP - 33

EP - 43

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -