Abstract
Consider 1 → S → E → G → 1, where G is a finite p-group generated by gi, 1 ≤ i ≤ d, and E a free product of cyclic groups$\langle g_i \rangle, 1 \leq i \leq d$. If d is the minimum number of generators for G, then we prove that the largest elementary abelian p-quotient S/S'Sp, regarded as an FpG-module via conjugation in E, is nonprojective and indecomposable.