RATIONAL SUBSETS IN HNN-EXTENSIONS AND AMALGAMATED PRODUCTS
Markus Lohrey, Géraud Sénizergues · International Journal of Algebra and Computation · 2008
Several transfer results for rational subsets and finitely generated subgroups of HNN-extensions G = 〈 H,t; t-1 at = φ(a) (a ∈ A) 〉 and amalgamated free products G = H *A J such that the associated subgroup A is finite. These transfer results allow to transfer decidability properties or structural properties from the subgroup H (resp. the subgroups H and J) to the group G.