Let FIR be a finitely generated recursively presented group with the solvable conjugacy problem and the solvable power problem. The conjugacy problem for F/R' when F/R is torsion free has been solved by Remeslennikov and Sokolov (Algebra and Logic 9 (1970), 342-349). In this note we prove that F/R' has the solvable conjugacy problem even when F/R is not torsion free. This allows us, in particular, to conclude the solvability of the conjugacy problem for F/[Fl, FI] in terms of the conjugacy problem for F/Fn. Summary. If the conjugacy problem and the power problem for F/R is solvable, then the conjugacy problem for F/R' is solvable. Introduction. Let F/R be a finitely generated recursively presented group with the solvable conjugacy problem and the solvable power problem. The conjugacy problem for F/R' when F/R is torsion free has been solved by Remeslennikov and Sokolov [6]. In this note we are able to prove that F/R' has the solvable conjugacy problem even when F/R is not torsion free. This allows us, in particular, to conclude the solvability of the conjugacy problem for F/[Fn, Fn] in terms of the conjugacy problem for F/FI. As in [6] our tool is the Magnus embedding of F/R' into a group of 2 X 2 matrices and a result of Matthews [5] about the conjugacy problem for the restricted wreath product of two groups. Pre iminary results. Let F be a noncyclic free group on a finite set X and R a normal subgroup of F. Let Ql be the free left Z(F/R)-module with basis {X$jx E X}. Then every element of Q2 is of the form fZE fxX fx E Z(F/R). xX For w E F, we set Rw = w and consider the group M F/R Q2 O RIR) of 2 X 2 matrices of the form (w f 0O 1) w E F, f E ?2. It is easily verified that M is isomorphic to the restricted wreath product of a free abelian group of rank IXI by F/R. Thus, by a result of Matthews [5], we have Received by the editors October 6, 1980. 1980 Mathematics Subject Classification. Primary 20F10. lResearch supported by the Natural Sciences and Engineering Research Council Canada. i) 1982 American Mathematical Society 0002-9939/81/0000-1066/$02.25 149 This content downloaded from 157.55.39.111 on Wed, 03 Aug 2016 05:17:24 UTC All use subject to http://about.jstor.org/terms