On the Cameron-Praeger Conjecture

Details On the Cameron-Praeger Conjecture On the Cameron-Praeger Conjecture

2009-04-21

arxiv.org/abs/0904.3239v1

Mathematics

Combinatorics

11 pages; to appear in: "Journal of Combinatorial Theory, Series A"

Scientific paper

This paper takes a significant step towards confirming a long-standing and far-reaching conjecture of Peter J. Cameron and Cheryl E. Praeger. They conjectured in 1993 that there are no non-trivial block-transitive 6-designs. We prove that the Cameron-Praeger conjecture is true for the important case of non-trivial Steiner 6-designs, i.e. for 6-$(v,k,\lambda)$ designs with $\lambda=1$, except possibly when the group is $P\GammaL(2,p^e)$ with $p=2$ or 3, and $e$ is an odd prime power.

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