Abstract commensurability and the Gupta–Sidki group

  • Alejandra Garrido

    Université de Genève, Switzerland


We study the subgroup structure of the infinite torsion -groups defined by Gupta and Sidki in 1983. In particular, following results of Grigorchuk and Wilson for the first Grigorchuk group, we show that all infinite finitely generated subgroups of the Gupta–Sidki 3-group are abstractly commensurable with or . As a consequence, we show that is subgroup separable and from this it follows that its membership problem is solvable.

Along the way, we obtain a characterization of finite subgroups of and establish an analogue for the Grigorchuk group.

Cite this article

Alejandra Garrido, Abstract commensurability and the Gupta–Sidki group. Groups Geom. Dyn. 10 (2016), no. 2, pp. 523–543

DOI 10.4171/GGD/355