Assouad-Nagata Dimension of Wreath Products of Groups

Canadian mathematical bulletin

U. Lang²  J. Dydak¹  N. Brodskiy¹ 

[1] Department of Mathematics, University of Tennessee, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996;Eidgen Technische Hochschule Zentrum, CH-8092 Zürich, Switzerland

关键词: Assouad-Nagata dimension;    asymptotic dimension;    wreath product;    growth of groups;   

DOI  :  10.4153/CMB-2013-024-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Consider the wreath product $Hwr G$, where $He 1$ is finite and $G$ is finitely generated.We show that the Assouad-Nagata dimension $dim_{AN}(Hwr G)$ of $Hwr G$depends on the growth of $G$ as follows:par If the growth of $G$ is not bounded by a linear function, then $dim_{AN}(Hwr G)=infty$,otherwise $dim_{AN}(Hwr G)=dim_{AN}(G)leq 1$.

【 授权许可】

Unknown