The virtual first Betti number of soluble groups

Martin R. Bridson and Dessislava H. Kochloukova

Vol. 274 (2015), No. 2, 497–510

DOI: 10.2140/pjm.2015.274.497

Abstract

We show that if a group $G$ is finitely presented and nilpotent-by-abelian-by-finite, then there is an upper bound on ${dim}_{\mathbb{Q}}{H}_1\left(M,\mathbb{Q}\right)$, where $M$ runs through all subgroups of finite index in $G$.

Keywords

soluble groups, virtual first betti number, nilpotent-by-abelian-by-finite

Mathematical Subject Classification 2010

Primary: 20F16, 20J05

Milestones

Received: 25 July 2014

Revised: 15 September 2014

Accepted: 18 September 2014

Published: 1 April 2015