A converse to a residual finiteness theorem of G. Baumslag
Mazi Shirvani · Proceedings of the American Mathematical Society · 1988
It is shown that if at least two of the factor groups of a nontrivial amalgamated free product G G satisfy nontrivial identities, then a special form of the profinite closure of the associated subgroups is necessary (as well as sufficient) for the residual finiteness of G G . An example shows that the necessity no longer holds if only one of the factor groups satisfies an identity.