  Adding two generators and one arbitrary relator to a nontrivial torsion-free
group, we always obtain an SQ-universal group. In the course of the proof of
this theorem, we obtain some other results of independent interest. For
instance, adding one generator and one relator in which the exponent sum of the
additional generator is one to a free product of two nontrivial torsion-free
groups, we also obtain an SQ-universal group.
  Key words: relative presentations, one-relator groups, SQ-universality,
equations over groups.
