The isomorphism problem for two-generator one-relator groups with torsion is solvable
Stephen J. Pride · Transactions of the American Mathematical Society · 1977
The theorem stated in the title is obtained by determining (in a sense to be made precise) all the generating pairs of an arbitrary two-generator one-relator group with torsion. As a consequence of this determination it is also deduced that every two-generator one-relator group G with torsion is Hopfian, and that the automorphism group of G is finitely generated.