Title

A Quasi-Isometry Invariant Loop Shortening Property for Groups

Document Type

Article

Publication Date

12-1-2008

Department

Mathematics

Abstract

We first introduce a loop shortening property for metric spaces, generalizing the property considered by M. Elder on Cayley graphs of finitely generated groups. Then using this metric property, we define a very broad loop shortening property for finitely generated groups. Our definition includes Elder's groups, and unlike his definition, our property is obviously a quasi-isometry invariant of the group. Furthermore, all finitely generated groups satisfying this general loop shortening property are also finitely presented and satisfy a quadratic isoperimetric inequality. Every CAT(0) cubical group is shown to have this general loop shortening property.

Publication Title

International Journal of Algebra and Computation

Volume

18

Issue

8

First Page

1243

Last Page

1257