Adrian M. Nelson

GBRDs over groups of orders ≤100 or of order p q with p, q primes

There are well-known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G, with block size k=3. It has been conjectured that these necessary conditions are indeed sufficient. We prove that they are sufficient for groups G of order pq where p,q are primes and for groups of all orders @?100 except possibly 32, 36, 48, 54, 60, 64, 72, 96.

GBRDs over supersolvable groups and solvable groups of order prime to 3

We show that the established necessary conditions for a GBRD

Block designs signed over groups of order 2n3m

{(v,3,\lambda; \mathbb {G})}

Magic labellings of graphs over finite abelian groups.

are sufficient (i) when

GBRDs with block size three over 2-groups, semi-dihedral groups and nilpotent groups

{\mathbb {G}}

GBRDs with block size 3 over odd order groups and groups of orders divisible by 2 but not 4

is supersolvable and (ii) when