Commentarii Mathematici Helvetici

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Volume 85, Issue 1, 2010, pp. 135–150
DOI: 10.4171/CMH/190

Virtually soluble groups of type FP

Conchita Martínez-Pérez[1] and Brita E. A. Nucinkis[2]

(1) Departamento de Matemáticas, Universidad de Zaragoza, C/Pedro Cerbuna, 12, 50009, Zaragoza, Spain
(2) Department of Mathematics, Royal Holloway University of London, Egham Hill, TW20 0EX, Egham, UK

We prove that a virtually soluble group G of type FP admits a finitely dominated model for EG of dimension the Hirsch length of G. This implies in particular that the Brown conjecture is satisfied for virtually torsion-free elementary amenable groups.

Keywords: Cohomological finiteness conditions, soluble groups

Martínez-Pérez Conchita, Nucinkis Brita E. A.: Virtually soluble groups of type FP. Comment. Math. Helv. 85 (2010), 135-150. doi: 10.4171/CMH/190