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 -