Equations in HNN-extensions.
Markus Lohrey, Géraud Sénizergues · 2008
Abstract. Let H be a cancellative monoid and let G be an HNN-extension of H with finite associated subgroups A,B ≤ H. We show that, if equations are algorithmically solvable in H, then they are also algorithmically solvable in G. The result also holds for equations with rational constraints and for the existential first order theory. Analogous results are derived for amalgamated product with finite amalgamated subgroups. Finally, a transfer theorem is shown for the fundamental group of a finite graph of groups with finite edge groups and vertex groups where the existential first-order theory is decidable. Keywords: Equations; groups and monoids; HNN-extensions; amalgamated product.