Monomorphisms of finitely generated free groups have finitely generated equalizers
If \(\phi\),\(\psi\) : \(G\to H\) are homomorphisms of groups, then the subgroup \(Eq(\phi,\psi)=\{x|\) \(\phi (x)=\psi (x)\}\) of G is called the equalizer of \(\phi\) and \(\psi\). The main result, which takes care of a conjecture of Stallings, is the following: If \(\phi\) and \(\psi\) are monomorphisms and G is a finitely generated free group, then Eq(\(\phi\),\(\psi)\) is finitely generated. The authors use graphical methods and prove all the main results in the 3-dimensional Whitehead model. They mention that \textit{J. Stallings} [Graphical Theory of automorphisms of Free Groups, Proc. Alto Conf. Comb. Group Theory] and \textit{D. Cooper} [Automorphisms of free groups have f.g. fixed point sets (preprint)] have also given a proof of this main result.
scientific article; zbMATH DE number 3931255
scientific article