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Article overview
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On asymptotic dimension of groups | G. Bell
; A. Dranishnikov
; | Date: |
2 Dec 2000 | Journal: | Algebraic and Geometric Topology 1 (2001) 57-71 | Subject: | Group Theory; Geometric Topology MSC-class: 20H15, 20E34, 20F69 | math.GR math.GT | Abstract: | We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdim A *_C B < infinity. B) Suppose that G’ is an HNN extension of a group G with asdim G < infinity. Then asdim G’< infinity. C) Suppose that Gamma is Davis’ group constructed from a group pi with asdimpi < infinity. Then asdimGamma < infinity. | Source: | arXiv, math.GR/0012006 | Services: | Forum | Review | PDF | Favorites |
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