Starting from desarguesian and twisted ยฎeld planes we construct and study some classes of divisible designs admitting an automorphism group which is 2-transitive on the set of point classes.
On divisible designs and local algebras
โ Scribed by Antonino Giorgio Spera
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 558 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
โฆ Synopsis
We study the action of the group PGL(m,A) on the projective space PG(ml , A ) over a finite commutative local algebra A in order to construct a class of divisible designs, denoted by D,(d,A), which is the classical one of 2-designs (of points and of flats of fixed projective dimension) in the case where A is a field. We also study the constructed divisible designs with particular care for the case where d = m -1. o 1995 John Wiley & Sons, Inc.
๐ SIMILAR VOLUMES
## Abstract We obtain new conditions on the existence of a square matrix whose Gram matrix has a block structure with certain properties, including Dโoptimal designs of order $n\equiv 3 \pmod 4$, and investigate relations to group divisible designs. We also find a matrix with large determinant for
We introduce weakly divisible MV-algebras and we show that every weakly divisible a-complete MV-algebra is isomorphic to the system of all continuous fuzzy functions defined on some compact Hausdorff space which generalizes a result of Di Nola and Sesse (in "Non Classical Logics and Their Applicatio
If D is a tame central division algebra over a Henselian valued field F, then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF. After proving some properties of graded central simple algebras over a graded field (inc