FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 3, PAGES 875-888
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 $2^k$ -th degrees and
terms of the Engel series are indicated precisely.
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