A converse to a residual finiteness theorem of G. Baumslag
A converse to a residual finiteness theorem of G. Baumslag
It is shown that if at least two of the factor groups of a nontrivial amalgamated free product <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfy nontrivial identities, then a special form of the profinite closure of the associated subgroups is necessary (as well …