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The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees |
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| Authors: | R I Grigorchuk J S Wilson |
| Institution: | (1) Steklov Mathematical Institute, Gubkina Street 8, Moscow, 119991, Russia;(2) School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, England |
| Abstract: | It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions. |
| Keywords: | group actions rooted trees basal subgroups vertex subgroups |
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