Finitely generated subgroups of branch groups and subdirect products of just infinite groups
Izvestiya. Mathematics , Tome 85 (2021) no. 6, pp. 1128-1145
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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.
@article{IM2_2021_85_6_a3,
author = {R. I. Grigorchuk and P.-H. Leemann and T. V. Nagnibeda},
title = {Finitely generated subgroups of branch groups and subdirect products of just infinite groups},
journal = {Izvestiya. Mathematics },
pages = {1128--1145},
publisher = {mathdoc},
volume = {85},
number = {6},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_6_a3/}
}
TY - JOUR AU - R. I. Grigorchuk AU - P.-H. Leemann AU - T. V. Nagnibeda TI - Finitely generated subgroups of branch groups and subdirect products of just infinite groups JO - Izvestiya. Mathematics PY - 2021 SP - 1128 EP - 1145 VL - 85 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_2021_85_6_a3/ LA - en ID - IM2_2021_85_6_a3 ER -
%0 Journal Article %A R. I. Grigorchuk %A P.-H. Leemann %A T. V. Nagnibeda %T Finitely generated subgroups of branch groups and subdirect products of just infinite groups %J Izvestiya. Mathematics %D 2021 %P 1128-1145 %V 85 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_2021_85_6_a3/ %G en %F IM2_2021_85_6_a3
R. I. Grigorchuk; P.-H. Leemann; T. V. Nagnibeda. Finitely generated subgroups of branch groups and subdirect products of just infinite groups. Izvestiya. Mathematics , Tome 85 (2021) no. 6, pp. 1128-1145. http://geodesic.mathdoc.fr/item/IM2_2021_85_6_a3/