Assouad-Nagata dimension of wreath products of groups

الأصل · EN

Consider the wreath product H G, where H≠ 1 is finite and G is finitely generated. We show that the Assouad-Nagata dimension (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 (H G)=∞, otherwise (H G)=(G)≤ 1.