On the Cameron–Praeger conjecture

• Published in: Journal of combinatorial theory. Series A Vol. 117; no. 2; pp. 196 - 203
• Main Author: Huber, Michael
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2010
• Subjects: 3-homogeneous permutation groups; Block-transitive group of automorphisms; Cameron–Praeger conjecture; Steiner designs; Cameron–Praeger conjecture; Steiner designs; 3-homogeneous permutation groups; Block-transitive group of automorphisms
• ISSN: 0097-3165; 1096-0899
• DOI: 10.1016/j.jcta.2009.04.004

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 , λ ) designs with λ = 1 , except possibly when the group is PΓL ( 2 , p e ) with p = 2 or 3, and e is an odd prime power.