On difference matrices of coset type

A ( u , k ; λ ) -difference matrix H over a group U is said to be of coset type with respect to one of its rows, say w, whose entries are not equal, if it has the property that rw is also a row of H for any row r of H. In this article we study the structural property of such matrices with u ( < k ) a prime and show that u | λ and, moreover, H contains u ( u , k / u ; λ / u ) -difference submatrices and is equivalent to a special kind of extension using them. Conversely, we also show that any set of u ( u , k ′ ; λ ′ ) -difference matrices over U yields a ( u , u k ′ ; u λ ′ ) -difference matrix of coset type over U.