Virtually soluble groups of type $\operatorname{FP}_∞$

Conchita Martínez-Pérez; Brita E. A. Nucinkis

doi:10.4171/cmh/190

JournalscmhVol. 85, No. 1pp. 135–150

Virtually soluble groups of type $FP_{\infty}$

Conchita Martínez-Pérez
Universidad de Zaragoza, Spain
Brita E. A. Nucinkis
Royal Holloway University of London, Egham, UK

$Virtually soluble groups of type $\operatorname{FP}_∞$ cover$

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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.

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Conchita Martínez-Pérez, Brita E. A. Nucinkis, Virtually soluble groups of type $FP_{\infty}$ . Comment. Math. Helv. 85 (2010), no. 1, pp. 135–150

DOI 10.4171/CMH/190