Structure of some relative relation modules of finite p-groups

Let G be a finite p-group generated by (gi, 1 ≤ i ≤ d), Gi the cyclic subgroup generated by gi, E the free product of the Gi, 1 ≤ i ≤ d, and S the kernel of the natural epimorphism of E onto G. The largest elementary abelian p-quotient S-circumflex = S/S'Sp, regarded as an IFpG-module via conjugation in E, is called a relative relation module of G. If d is the minimum number of generaters for G, the author has proved that S-circumflex is nonprojective and indecomposable. The aim of this paper is to give an alternative proof for the indecomposability of S-circumflex; the proof here is more informative as it deals with Loewy structure and generating sets of S-circumflex and other associated modules. (author). 9 refs