Let M be the group defined by the presentation 〈 x, y, z | xy = xm, yz = yn, zx = zr〉,m,n,r ∊ Z. M is one of the few 3-generator finite groups of deficiency zero. These groups have been considered by Mennicke , Macdonald, Wamsley , Johnson and Robertson , and Albar. Properties like the order of M, the nilpotency and solvability were studied. In this paper we give a better upper bound for M than the one given by Johnson and Robertson . We also describe the structure of some cases of M.