Finitely generated subgroups of branch groups and subdirect products of just infinite groups

R. I. Grigorchuk ; P.-H. Leemann ; T. V. Nagnibeda

Izvestiya. Mathematics , Tome 85 (2021) no. 6, pp. 1128-1145.

Résumé

The aim of this paper is to describe the structure of finitely generated subgroups of a family of branch groups containing the first Grigorchuk group and the Gupta–Sidki $3$-group. We then use this to show that all the groups in this family are subgroup separable (LERF). These results are obtained as a corollary of a more general structural statement on subdirect products of just infinite groups.

Détail

Keywords: just infinite groups, subdirect products, branch groups.

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