arXiv:2006.16121 Abstract | arXiv Analytics

arXiv:2006.16121 [math.GR]Abstract References Reviews Resources

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

Rostistlav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda

Published 2020-06-29Version 1

The aim of this paper is to describe the structure of the finitely generated subgroups of a family of branch groups, which includes the first Grigorchuk group and the Gupta-Sidki 3-group. This description is made via the notion of block subgroup. We then use this to show that all groups in the above 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.

Comments: 22 pages, 2 figures

Categories: math.GR

Subjects: 20E07, 20E08, 20E28

Keywords: finitely generated subgroups, infinite groups, branch groups, subdirect products, general structural statement

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