Assouad-Nagata dimension of wreath products of groups

2006/11/11 by N. Brodskiy, J. Dydak, Brodskiy, N. +5
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #math.GR #math.GT #math.MG

paper · pdf · doi:10.48550/arxiv.math/0611331

11 pages, new references added

openalex publication_date 2006/11/11 · arxiv created 2006/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the wreath product H\wr G, where H≠ 1 is finite and G is finitely generated. We show that the Assouad-Nagata dimension dim_AN(H\wr G) of H\wr G depends on the growth of G as follows: If the growth of G is not bounded by a linear function, then dim_AN(H\wr G)=∞, otherwise dim_AN(H\wr G)=dim_AN(G)≤ 1.

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