Largeness of LERF and 1-relator groups

  • Jack Oliver Button

    University of Cambridge, UK


We consider largeness of groups given by a presentation of deficiency , where the group is respectively free-by-cyclic, LERF or 1-relator. We give the first examples of (finitely generated free)-by- word hyperbolic groups which are large, show that a LERF deficiency 1 group with first Betti number at least two is large or and show that 2-generator 1relator groups where the relator has height obey the dichotomy that either the group is large or all its finite images are metacyclic.

Cite this article

Jack Oliver Button, Largeness of LERF and 1-relator groups. Groups Geom. Dyn. 4 (2010), no. 4, pp. 709–738

DOI 10.4171/GGD/102