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

N. V. Smetanyuk^a, V. I. Sushchanskii<sup>b

a</sup> National Taras Shevchenko University of Kyiv
^b Silesian University of Technology

Abstract: 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.

UDC: 512.54

Received: 01.10.1999

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