A finitely presented HNN-extension example: Non-finitely generated groups, and an application of small cancellation theory

AbstractThis paper gives an example of a finitely generated group G and a monomorphism α : G→G such that ⋂n αn(G) is not finitely generated. Such examples are potential counterexamples to a variety of conjectures in the study of the cohomology and end-theory of groups. The techniques of small cancellation theory are combined with a simple characterization of non-finitely generated groups to give a method for producing more examples of this general type