RELATIVE RELATION MODULES OF FINITE ELEMENTARY ABELIAN p-GROUPS

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that E/S congruent to G is finite. For a prime p, 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 (S) over cap is decomposable into two indecomposable modules for finite elementary abelian p-groups G.