RELATIVE RELATION MODULES OF FINITE ELEMENTARY ABELIAN p-GROUPS

Abstract

Abstract. Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that E/S ∼ = G is finite. For a prime p,Ŝ = S/S ′ S p may be regarded as an FpG-module via conjugation in E. The aim of this article is to prove thatŜ is decomposable into two indecomposable modules for finite elementary abelian p-groups G.