Sufficient conditions for the root-class residuality of certain generalized free products

详细

Given a class K of groups, we prove that the free product of a K -group A and a residually K -group B with amalgamated subgroup which is a retract of B is a residually K -group. We also obtain a sufficient condition for the root-class residuality of a generalized free product of two residually K -groups with amalgamated subgroup which is a retract of one of the factors.