The virtual first betti number of soluble groups

Martin R. Bridson and Dessislava H. Kochloukova

We show that if a group G is finitely presented and nilpotent-by-abelian-by-finite, then there is an upper bound on the first betti number of M as M runs through all subgroups of finite index in G.

To appear in Pacific Journal of Math

11 pages, no figures.