We prove that in a self-similar wreath product of abelian groups G=B wr X, if X is torsion-free then B is torsion of finite exponent. Therefore, in particular, the group Z wr Z cannot be self-similar. Furthemore, we prove that if L is a self-similar abelian group then Lω wr C2 is also self-similar.
Classification :
20-XX
Mots-clés :
Automorphisms of trees, state-closed groups, self-similar groups
Affiliations des auteurs :
Alex C. Dantas
1
;
Said N. Sidki
2
1
Universidade Tecnológica Federal do Paraná, Guarapuava, Brazil
2
Universidade de Brasilia, Brazil
Alex C. Dantas; Said N. Sidki. On self-similarity of wreath products of abelian groups. Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 1061-1068. doi: 10.4171/ggd/462
@article{10_4171_ggd_462,
author = {Alex C. Dantas and Said N. Sidki},
title = {On self-similarity of wreath products of abelian groups},
journal = {Groups, geometry, and dynamics},
pages = {1061--1068},
year = {2018},
volume = {12},
number = {3},
doi = {10.4171/ggd/462},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/462/}
}
TY - JOUR
AU - Alex C. Dantas
AU - Said N. Sidki
TI - On self-similarity of wreath products of abelian groups
JO - Groups, geometry, and dynamics
PY - 2018
SP - 1061
EP - 1068
VL - 12
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/462/
DO - 10.4171/ggd/462
ID - 10_4171_ggd_462
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%J Groups, geometry, and dynamics
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/462/
%R 10.4171/ggd/462
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