Geodesic
Abstract commensurability and the Gupta–Sidki group
Alejandra Garrido1 orcid
1Université de Genève, Switzerland
Groups, geometry, and dynamics, Tome 10 (2016) no. 2, pp. 523-543

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DOI

We study the subgroup structure of the infinite torsion p-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 G are abstractly commensurable with G or G×G. As a consequence, we show that G is subgroup separable and from this it follows that its membership problem is solvable.
DOI : 10.4171/ggd/355
Classification : 20-XX
Mots-clés : Abstractly commensurable, structure of finitely generated subgroups, subgroup separable (LERF), Gupta–Sidki groups

Alejandra Garrido  1

1 Université de Genève, Switzerland 
Alejandra Garrido. Abstract commensurability and the Gupta–Sidki group. Groups, geometry, and dynamics, Tome 10 (2016) no. 2, pp. 523-543. doi: 10.4171/ggd/355
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     title = {Abstract commensurability and the {Gupta{\textendash}Sidki} group},
     journal = {Groups, geometry, and dynamics},
     pages = {523--543},
     year = {2016},
     volume = {10},
     number = {2},
     doi = {10.4171/ggd/355},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/355/}
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