Semiregular group divisible designs whose duals are semiregular

ABSTRAC"T A construction method for semiregular group divisible designs is given. This method can be applied to yield many classes of (in general, non-symmetric) semiregular group divisible designs whose duals are semiregular group divisible. In particular, the method can be used to construct many classes of transversal designs whose duals are serniregular group divisible designs, but not transversal designs. Also, some of the semiregular group divisible designs the construction method yields can be used to construct self-dual regular group divisible designs with two groups of points and blocks. Four infinite classes of such regular group divisible designs are constructed.