Limits of Baumslag–Solitar groups

Abstract

We give a parametrization by m-adic integers of the limits of Baumslag–Solitar groups (marked with a canonical set of generators). It is shown to be continuous and injective on the invertible m-adic integers. We show that all such limits are extensions of a free group by a lamplighter group and all but possibly one are not finitely presented. Finally, we give presentations related to natural actions on trees.