On Finitely Generated Subgroups of Free Products

Abstract

IfHis a subgroup of a groupGwe shall say thatGisH-residually finiteif for every elementginG, outsideH, there is a subgroup of finite index inG, containingHand still avoidingg. (Then, according to the usual definition,Gisresidually finiteif it isE-residually finite, whereEis the identity subgroup). Definitions of other terms used below may be found in § 2 or in [6].