ON ROOT CLASS RESIDUALITY OF HNN-EXTENSIONS

Abstract. A sufficient condition for root-class residuality of HNN-extensions with root-class residual base group is proven; namely if G = 〈A, t; t−1Ht = K,ϕ 〉 is the HNN-extension with base group A, stable letter t and associated subgroups H and K via the isomorphism ϕ, then G is root-class residual if group A is root-class residual and there exists a homomorphism σ of group G onto some group of a root-class such that σ is one-to-one on H. For the particular case when H = K and ϕ is the identity map, it is shown that G is root-class residual if and only if A is root-class residual and subgroup H of A is root-class separable. These results are generalized to multiple HNN-extensions. Acknowlegment: This work was carried out at the Mathematics Section of the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste (Italy) during the author’s visit in summer 2004. The author gratefully acknowledges the financial sup-port from the ICTP and the International Mathematical Union (IMU) CDE Exchange programme for this visit