Isomorphism problem for finitely generated fully residually free groups
  We prove that the isomorphism problem for finitely generated fully residually free groups is decidable. We also show that each finitely generated fully residually free group G has a decomposition that is invariant under automorphisms of G, and obtain a structure theorem for the group of outer automorphisms Out(G). 
Inna Bumagin, Olga Kharlampovich and Alexei Miasnikov