Codimension-1 Subgroups and Splittings of Groups

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, termi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 1997-03, Vol.189 (2), p.377-389
Main Author: Sageev, Michah
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1006/jabr.1996.6884