Next: Introduction
Partitioned Steiner 5-Designs
Reinhard Laue, Alfred Wassermann,
University of Bayreuth, Germany
Abstract:
Orbits of
on 6-element subsets of the projective line with
prescribed non-trivial stabilizer are described. A refinement of cross-ratio
computations to
orbits allows to determine the orbits on
5-element subsets that they cover. Then Steiner
-
designs
are assembled from them. In particular, there is one isomorphism type
of
-
designs that consists of
orbits of the same size,
each being a
-
design. There are 7 isomorphism types
of
-
designs of this type. Generally, Steiner
-
designs
with such an orbit partition may only exist if
.
![$PSL(2,p)$](img1.png)
![$PSL(2,p)$](img1.png)
![$5$](img2.png)
![$(p+1,6,1)$](img3.png)
![$5$](img2.png)
![$(48,6,1)$](img4.png)
![$PSL(2,p)$](img1.png)
![$3$](img5.png)
![$(48,6,30)$](img6.png)
![$5$](img2.png)
![$(84,6,1)$](img7.png)
![$5$](img2.png)
![$(p+1,6,1)$](img3.png)
![$p\equiv 48,\ 84\ mod \ 180$](img8.png)
- Introduction
- Basic Conditions
- Subgroups of order up to 6 in
- Invariants
- Bibliography
- About this document ...
N.N. 2002-02-25