Distortion of wreath products in some finitely presented groups

Sean Cleary

Vol. 228 (2006), No. 1, 53–61

DOI: 10.2140/pjm.2006.228.53

Abstract

Wreath products such as ℤ ≀ ℤ are not finitely presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of ℤ ≀ ℤ as a subgroup of Thompson’s group F and as a subgroup of Baumslag’s metabelian group G. We find that ℤ ≀ ℤ is undistorted in F but is at least exponentially distorted in G.

Keywords

subgroup distortion, Thompson’s group

Mathematical Subject Classification 2000

Primary: 20F65

Milestones

Received: 28 January 2005

Accepted: 17 March 2006

Published: 1 November 2006