Block-transitive t-designs I: point-imprimitive designs
نویسندگان
چکیده
منابع مشابه
A note on block-transitive point-imprimitive designs
We study block-transitive point-imprimitive designs. Cameron and Praeger showed that in such designs t = 2 or 3. In 2000, Mann and Tuan showed that if t = 3 then v ≤ (k2) + 1. In this paper, we show a finiteness theorem for block-transitive point-imprimitive 3-designs for which this bound is met. We prove that for a given natural number n, there are only finitely many numbers k of the form npα ...
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A recent paper of O’Reilly Regueiro obtained an explicit upper bound on the number of points of a flagtransitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of...
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By a resolution of t-designs we mean a partition of the trivial design ? X k of all k-subsets of a v-set X into t ? (v 0 ; k;) designs, where v 0 v. A resolution of t-designs with v = v 0 is also called a large set of t-designs. A Room rectangle R, based on ? X k , is a rectangular array whose non-empty entries are k-sets. This array has the further property that taken together the rows form a ...
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This paper deals with block-transitive t-(v, k, λ) designs in affine spaces for large t, with a focus on the important index λ = 1 case. We prove that there are no non-trivial 5-(v, k, 1) designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-(v, k, 1) designs, except possibly when the group i...
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Let $G$ be an automorphism group of a $2$-$(v,k,4)$ symmetric design $mathcal D$. In this paper, we prove that if $G$ is flag-transitive point-primitive, then the socle of $G$ cannot be an exceptional group of Lie type.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90051-t