Intersections of Magnus subgroups and embedding theorems for cyclically   presented groups
  A Magnus subgroup of a one-relator group is the free subgroup freely generated by a proper subset of the generators. Two such subgroups can intersect in the obvious way or in a larger, exceptional way. The condition of non-exceptional intersection of Magnus subgroups of a one-relator group is applied to give criteria for the resulting cyclically presented groups to contain nonabelian free subgroups. 
Martin Edjvet and James Howie