Abstract:
The finitely generated centralizers of elements in the Grigorchuk 2-group are described (answering a question of Lennox). The double centralizers of elements and the centralizers of involutions are studied. An analogue of the congruence problem is solved affirmatively. The indices of congruence subgroups and the terms of the commutator series are calculated.
\Bibitem{Roz93}
\by A.~V.~Rozhkov
\paper Centralizers of elements in a group of tree automorphisms
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 43
\issue 3
\pages 471--492
\mathnet{http://mi.mathnet.ru/eng/im827}
\crossref{https://doi.org/10.1070/IM1994v043n03ABEH001639}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1256568}
\zmath{https://zbmath.org/?q=an:0829.20056}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..43..471R}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994QK21500005}
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