On self-similarity of wreath products of abelian groups

被引：5

作者：

Dantas, Alex C. ^{[1
]}

Sidki, Said N. ^{[2
]}

机构：

[1] Univ Tecnol Fed Parana, BR-85053525 Guarapuava, PR, Brazil

[2] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

GROUPS GEOMETRY AND DYNAMICS | 2018年 / 12卷 / 03期

关键词：

Automorphisms of trees; state-closed groups; self-similar groups;

D O I：

10.4171/GGD/462

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. Furthermore, we prove that if L is a self-similar abelian group then L-omega wr C-2 is also self-similar.

引用

页码：1061 / 1068

页数：8

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