Virtually soluble groups of type FP∞

Conchita Martinez-Pérez; Brita E.A. Nucinkis

doi:10.4171/CMH/190

Virtually soluble groups of type FP∞

Conchita Martinez-Pérez
, Brita E.A. Nucinkis

Research output: Contribution to journal › Article › peer-review

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Abstract

We prove that a virtually soluble group $G$ of type $FP_\infty$
admits a finitely dominated model for $\underline{E}G$ of dimension the Hirsch
length of $G$. This implies in particular that the Brown conjecture
is satisfied for virtually torsion-free elementary amenable groups.

Original language	English
Pages (from-to)	135-150
Number of pages	16
Journal	Commentarii Mathematici Helvetici
Volume	85
Issue number	1
DOIs	https://doi.org/10.4171/CMH/190
Publication status	Published - 2010

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MartinezNucinkisMarch08Submitted manuscript, 197 KB

http://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=85&iss=1&rank=5

Cite this

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title = "Virtually soluble groups of type FP∞",

abstract = "We prove that a virtually soluble group \$G\$ of type \$FP\_\textbackslash{}infty\$ admits a finitely dominated model for \$\textbackslash{}underline\{E\}G\$ of dimension the Hirsch length of \$G\$. This implies in particular that the Brown conjecture is satisfied for virtually torsion-free elementary amenable groups.",

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AB - We prove that a virtually soluble group $G$ of type $FP_\infty$ admits a finitely dominated model for $\underline{E}G$ of dimension the Hirsch length of $G$. This implies in particular that the Brown conjecture is satisfied for virtually torsion-free elementary amenable groups.

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DO - 10.4171/CMH/190

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EP - 150

JO - Commentarii Mathematici Helvetici

JF - Commentarii Mathematici Helvetici

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