Assouad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics

Higes, J.

doi:10.1090/S0002-9939-10-10240-8

Assouad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics
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Proc. Amer. Math. Soc. 138 (2010), 2235-2244 Request permission

Abstract:

Suppose $G$ is a countable, not necessarily finitely generated, group. We show $G$ admits a proper, left invariant metric $d_G$ such that the Assouad-Nagata dimension of $(G,d_G)$ is infinite, provided the center of $G$ is not locally finite. As a corollary we solve two problems of A. Dranishnikov.

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