A cyclically pinched product of free groups which is not residually free (Q1319305)

Let \(A\) and \(B\) be free groups of rank 2 and \(w_ 1\), \(w_ 2\) be words in \(A\) and \(B\), respectively, which are neither primitive nor proper powers. Two examples are given to show that the free product of \(A\) and \(B\) amalgamating \(w_ 1\) and \(w_ 2\) need not be residually free. This is in contrast with a result of G. Baumslag that if \(\alpha: A\to B\) is an isomorphism such that \(\alpha(w_ 1) =w_ 2\), then the free product of \(A\) and \(B\) amalgamating \(w_ 1\) and \(w_ 2\) is residually free.