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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Last modified: December 8, 2000