Abstract
Let G be a group and H be a subgroup of G. A complete description of Delta(G)Delta(n)(H)/Delta(n+1)(H) is given, and as a consequence the structures of Delta(G)/Delta(H) and Delta(2)(G)/Delta(2)(H) are determined. Also, the structure of Delta(n)(G)/Delta(n)(H) for all n >= 1 is determined when G is a free group.