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.
Cite this article
Luc Guyot, Yves Stalder, Limits of Baumslag–Solitar groups. Groups Geom. Dyn. 2 (2008), no. 3, pp. 353–381DOI 10.4171/GGD/44