RELATIVE RELATION MODULES OF FINITE-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 triple-over-dot = S/S'S(p) may be regarded as an F(p)G-module. Whenever E is a free group, S triple-over-dot is called a relation module (modulo p); in general we call S triple-over-dot a relative relation module (modulo p). Gaschutz, Gruenberg and others have studied relation modules; the aim of this paper is to study relative relation modules.