FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 3, PAGES 875-888

Verbal subgroups of the finitary automorphism group of a 2-adic tree

N. V. Smetaniuk
V. I. Sushchansky

Abstract

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It is established that any verbal subgroup of the group of finitary automorphisms of a 2-adic rooted tree coincides with some term of its lower central series. The coincidences for derived subgroups, subgroups of 2k-th degrees and terms of the Engel series are indicated precisely.


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