Additivity of symmetric and subspace 2-designs.

A 2- (v , k , λ) design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG d (n , q) , which was known to be additive only for q = 2 or d = n - 1 , is always established. [ABSTRACT FROM AUTHOR]