On Finitely Generated Subgroups of Free Products

Abstract

If H is a subgroup of a group G we shall say that G is H-residually finite if for every element g in G , outside H , there is a subgroup of finite index in G , containing H and still avoiding g . (Then, according to the usual definition, G is residually finite if it is E -residually finite, where E is the identity subgroup). Definitions of other terms used below may be found in § 2 or in [6].