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Asymptotic dimension of discrete groups

A. Dranishnikov; J. Smith — 2006

Fundamenta Mathematicae

We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for the asymptotic dimension of finitely generated solvable groups in terms of their Hirsch length.

On asymptotic dimension of groups.

Bell, G.; Dranishnikov, A. — 2001

Algebraic & Geometric Topology

On a formula for the asymptotic dimension of free products

G. C. Bell; A. N. Dranishnikov; J. E. Keesling — 2004

Fundamenta Mathematicae

We prove an exact formula for the asymptotic dimension (asdim) of a free product. Our main theorem states that if A and B are finitely generated groups with asdim A = n and asdim B ≤ n, then asdim (A*B) = max n,1.

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