Note: On the Cameron--Praeger conjecture

Authors:
Michael Huber
Affiliations:
Wilhelm-Schickard-Institute for Computer Science, University of Tuebingen, Sand 13, D-72076 Tuebingen, Germany
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

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Abstract

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,@l) designs with @l=1, except possibly when the group is P@CL(2,p^e) with p=2 or 3, and e is an odd prime power.