On the Cameron–Praeger conjecture
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...
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| Published in | Journal of combinatorial theory. Series A Vol. 117; no. 2; pp. 196 - 203 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.02.2010
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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
,
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. |
|---|---|
| AbstractList | 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. |
| Author | Huber, Michael |
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| Cites_doi | 10.1007/BF01109876 10.1112/plms/s3-54.3.477 10.1007/s10801-006-0053-0 10.1007/BF01112361 10.1007/BF01113919 10.1112/blms/13.1.1 10.1007/BF01111716 10.1007/s10801-007-0065-4 10.1006/jcta.2002.3305 10.1006/jcta.2000.3141 10.1016/0097-3165(85)90022-6 10.1515/advg.2005.5.2.195 10.1006/jcta.1998.2897 10.2140/pjm.1965.15.13 |
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| Keywords | Cameron–Praeger conjecture Steiner designs 3-homogeneous permutation groups Block-transitive group of automorphisms |
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| Title | On the Cameron–Praeger conjecture |
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