Bulletin of the
Korean Mathematical Society BKMS

Let $E$ be a free product of a finite number of cyclic groups, and $S$ a normal subgroup of E such that $E/S \cong G$ is finite. For a prime $p$, $\hat{S} = S/S^{'}S^{p}$ may be regarded as an $F_{p}G$-module via conjugation in $E$. The aim of this article is to prove that $\hat{S}$ is decomposable into two indecomposable modules for finite elementary abelian $p$-groups $G$.

Keywords: free groups, free products, $p$-groups, modules, relation modules

MSC numbers: 20C05, 16D10, 16D70