Groups, Geometry, and Dynamics

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Volume 2, Issue 3, 2008, pp. 353–381
DOI: 10.4171/GGD/44

Published online: 2008-09-30

Limits of Baumslag–Solitar groups

Luc Guyot[1] and Yves Stalder[2]

(1) Universität Göttingen, Germany
(2) Université Blaise Pascal, Aubière, France

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.

Keywords: Baumslag–Solitar groups, space of marked groups, Haagerup property, residual solvability

Guyot Luc, Stalder Yves: Limits of Baumslag–Solitar groups. Groups Geom. Dyn. 2 (2008), 353-381. doi: 10.4171/GGD/44