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.
Reviewer: S.Andreadakis


20E36 Automorphisms of infinite groups
20E05 Free nonabelian groups
Full Text: DOI EuDML


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