## Monomorphisms of finitely generated free groups have finitely generated equalizers.(English)Zbl 0582.20023

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 J. Stallings [Graphical Theory of automorphisms of Free Groups, Proc. Alto Conf. Comb. Group Theory] and D. Cooper [Automorphisms of free groups have f.g. fixed point sets (preprint)] have also given a proof of this main result.