R. I. Grigorchuk, P.-H. Leemann, T. V. Nagnibeda, “Finitely generated subgroups of branch groups and subdirect products of just infinite groups”, Izv. RAN. Ser. Mat., 2021, Volume 85, Issue 6,Pages <nobr>104

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

R. I. Grigorchuk^a, P.-H. Leemann^b, T. V. Nagnibeda^cd

^a Mathematical Department, Texas A&M University, USA
^b Institut de Mathématiques, Université de Neuchâtel, Neuchâtel, Switzerland
^c Section de mathématiques, Université de Genève, Genève, Switzerland
^d Saint Petersburg State University

Abstract: 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.

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

UDC: 512.544.2

MSC: 20E08, 20E18, 20F07, 20F10, 20F22, 37B05

Received: 05.09.2020

DOI: 10.4213/im9101