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.
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Grigorchuk, R.I., Wilson, J.S. The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees. Geometriae Dedicata 100, 103–116 (2003). https://doi.org/10.1023/A:1025851804561
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DOI: https://doi.org/10.1023/A:1025851804561