The genus of HNN‐extensions

Abstract

We find a bound on the genus of an HNN‐extension HNN(K, A, f) with a finite base group K. We also give sufficient conditions when the genus is 1, i.e. when HNN(K, A, f) is determined by its profinite completion up to isomorphism with respect to the family of all virtually free groups.

Genus for groups

“…Two non-isomorphic HNN-extensions with finite groups as base groups with the same profinite completion can be found in [4].…”

“…We shall give only few results with short proofs here. The reader may consult [4] for a more detailed investigation on the subject. We recall the definition of HNN-extensions.…”