Displaying similar documents to “On a formula for the asymptotic dimension of free products”

Asymptotic dimension of discrete groups

A. Dranishnikov, J. Smith (2006)

Fundamenta Mathematicae

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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.

The asymptotic dimension of the first Grigorchuk group is infinity.

Justin Smith (2007)

Revista Matemática Complutense

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We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.

Asymptotic dimension of one relator groups

Dmitry Matsnev (2008)

Colloquium Mathematicae

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We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov, and we give an improved estimate of that dimension in terms of the relator length. The construction is similar to one of Bell and Dranishnikov, but we produce a sharper estimate.