Assuad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics
classification
🧮 math.MG
math.GRmath.GT
keywords
dimensionadmitsarbitraryassouad-nagataassuad-nagatacentercorollarycountable
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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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