In this paper, we prove that the concepts of cocyclic Hadamard matrix
and Hadamard group are equivalent. A general procedure for constructin
g Hadamard groups and classifying such groups on the basis of isomorph
ism type is given. To illustrate the ideas, cocyclic Hadamard matrices
over dihedral groups are constructed and the corresponding Hadamard g
roups classified. (C) 1997 Academic Press.