Polynomial Maps over p-Adics and Residual Properties of Mapping Tori of Group Endomorphisms

This paper is a continuation of paper [1] where we proved that for every linear finitely generated group G and any injective endomorphism φ of G, the mapping torus of φ is residually finite. The mapping torus of φ is the following ascending HNN extension of G: HNNφ (G) = 〈G, t | txt−1 = φ(x)〉 where x runs over a (finite) generating set of G. Probably, the most important mapping tori are mapping tori of endomorphisms of free groups Fk. These groups appear frequently as fundamental groups of hyperbolic 3-manifolds (in fact there is a conjecture that all fundamental groups of hyperbolic 3manifolds are virtually mapping tori of free group automorphisms). Also it is proved in [8], that with probability tending to 1 as n → ∞, every 1-related group with three or more generators and relator of length n is embeddable into the mapping torus of a free group endomorphism (and so it is residually finite by [1, Theorem 1.6] and coherent by