Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 3, pp. 875-888
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N. V. Smetanyuk; V. I. Sushchanskii. Verbal subgroups of the finitary automorphism group of a $2$-adic tree. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 3, pp. 875-888. http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a17/
@article{FPM_2000_6_3_a17,
author = {N. V. Smetanyuk and V. I. Sushchanskii},
title = {Verbal subgroups of the finitary automorphism group of a $2$-adic tree},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {875--888},
year = {2000},
volume = {6},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a17/}
}
TY - JOUR
AU - N. V. Smetanyuk
AU - V. I. Sushchanskii
TI - Verbal subgroups of the finitary automorphism group of a $2$-adic tree
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2000
SP - 875
EP - 888
VL - 6
IS - 3
UR - http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a17/
LA - ru
ID - FPM_2000_6_3_a17
ER -
%0 Journal Article
%A N. V. Smetanyuk
%A V. I. Sushchanskii
%T Verbal subgroups of the finitary automorphism group of a $2$-adic tree
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2000
%P 875-888
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a17/
%G ru
%F FPM_2000_6_3_a17
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.
