Assouad-nagata Dimension of Wreath Products of Groups

  title={Assouad-nagata Dimension of Wreath Products of Groups},
  author={N Brodskiy and J Dydak and U Lang},
  • N Brodskiy, J Dydak, U Lang
  • Published 2008
Consider the wreath product H ≀ G, where H 6= 1 is finite and G is finitely generated. We show that the AssouadNagata dimension dimAN(H ≀ G) of H ≀ G depends on the growth of G as follows: If the growth of G is not bounded by a linear function, then dimAN (H ≀ G) = ∞, otherwise dimAN (H ≀ G) = dimAN (G) ≤ 1. Date: April 10, 2008. 2000 Mathematics Subject Classification. Primary 54F45; Secondary 55M10, 54C65.