Abstract
The lower central series of the Grigorchuk 3-generated 2-group is described; the indices of the factors of this series are calculated. The nilpotent length and solvability length of the factors by congruence subgroups are determined.
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R. I. Grigorchuk, “On Burnside's periodic group problem,”Funktsional. Anal, i Prilozhen. [Functional Anal. Appl.],14, 273–276 (1980).
A. V. Rozhkov, “Centralizers of elements in one group of tree automorphisms,”Izv. Ross. Akad. Nauk Ser. Mat. [Math. Izv.],57, No. 6, 85–102 (1993).
A. V. Rozhkov, “On the theory of Aleshin type groups,”Mat. Zametki [Math. Notes],40, No. 5, 572–589 (1986).
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Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 225–237, August, 1996.
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Rozhkov, A.V. Lower central series of a group of tree automorphisms. Math Notes 60, 165–174 (1996). https://doi.org/10.1007/BF02305180
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DOI: https://doi.org/10.1007/BF02305180