Elsevier

Journal of Algebra

Volume 189, Issue 2, 15 March 1997, Pages 377-389
Journal of Algebra

Regular Article
Codimension-1 Subgroups and Splittings of Groups

https://doi.org/10.1006/jabr.1996.6884Get rights and content
Under an Elsevier user license
open archive

Abstract

We show that under certain circumstances, a codimension-1 subgroupHof a finitely generated groupGeither provides a splitting ofGas an amalgam or provides a codimension-1 subgroup ofH. In particular, ifGis hyperbolic andHis quasiconvex, one gets a descending sequence of codimension-1 subgroups, terminating at a splitting. In the process, we settle a conjecture of Kropholler and Roller for the case of quasiconvex subgroups of hyperbolic groups.

Cited by (0)

Communicated by Peter, M. Neumann

*

Work partially supported by EPSERC grant GR/K25618. E-mail: [email protected].