Divisible designs with dual translation group

Divisible designs with dual translation group

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space. AMS Classification: 05B05, 05B30, 20B25, 51N10

Resolvable Group Divisible Designs with Large Groups

We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete mult...

Construction of Group Divisible Designs

Construction of Divisible Designs from Translation Planes

We construct some classes of divisible designs from nite translation planes of dimension two and three over GF(q), q a prime power, admitting SL(2; q) as a collineation group.

Divisible designs from twisted dual numbers

The generalized chain geometry over the local ring K(ε;σ) of twisted dual numbers, where K is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as well as a geometric model in 4-space are investigated. Mathematics Subject Classification (2000): 51E05, 51B15, 51E20, 51E25, 51A45.