Amalgam decompositions for one-relator groups (Q1304887)

Let \(G\) be a finitely presented group. A decomposition (if it exists) of \(G\) as a proper free product with amalgamation \((A*B:C)\) with the factors \(A\) and \(B\) and the amalgamated subgroup \(C\) all finitely generated is called a Baumslag-Shalen decomposition. It is known that \(G\) has a Baumslag-Shalen decomposition if the deficiency of \(G\) is greater than one. Especially, a one-relator group \(G\) with at least three generators admits a Baumslag-Shalen decomposition. In this latter special situation the authors prove some results about the exact nature of the factors \(A\) and \(B\) of the decomposition.