Commentarii Mathematici Helvetici
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Virtually soluble groups of type FP∞Conchita Martínez-Pérez and Brita E. A. Nucinkis (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