Left Ordered Amenable and Locally Indicable Groups

There has been interest recently concerning when a left orderedgroup is locally indicable. Chiswell and Kropholler proved thatevery left ordered solvable-by-finite group is locally indicable,while Bergman gave examples of left ordered groups which arenot locally indicable. This paper proves that every left orderedelementary amenable group is locally indicable. Every solvable-by-finitegroup is elementary amenable, and every elementary amenablegroup is amenable. The author leaves it as an open problem asto whether every left ordered amenable group is locally indicable.     

Whitehead groups and the Bass conjecture

This paper will be concerned with proving that certain Whitehead groups of torsion-free elementary amenable groups are torsion groups and related results, and then applying these results to the Bass conjecture. In particular we shall establish the strong Bass conjecture for an arbitrary elementary amenable group. Mathematics Subject Classification (2000): 19A31, 19B28, 16A27, 16E20, 20C07The first author was supported in part by the National Science Foundation     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups

We determine the L ²-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L ²-cohomology of left-orderable groups, and deduce the non-L ² result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613.