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Cohomological finiteness properties of the Brin–Thompson–Higman groups 2V and 3V

Part of: Connections with homological algebra and category theory

Published online by Cambridge University Press:  10 July 2013

Dessislava H. Kochloukova ,
Conchita Martínez-Pérez  and
Brita E. A. Nucinkis
Dessislava H. Kochloukova
Affiliation:
Department of Mathematics, University of Campinas, 13083-859 Campinas, São Paulo, Brazil ([email protected])
Conchita Martínez-Pérez
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain ([email protected])
Brita E. A. Nucinkis
Affiliation:
School of Mathematics, University of Southampton, University Road, Southampton SO17 1BJ, UK
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Abstract

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We show that Brin's generalizations 2V and 3V of the Thompson–Higman group V are of type FP∞. Our methods also give a new proof that both groups are finitely presented.

Keywords

cohomological finiteness conditionsgeneralized Thompson's groups

MSC classification

Secondary: 20J05: Homological methods in group theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 3 , October 2013 , pp. 777 - 804
Copyright
Copyright © Edinburgh Mathematical Society 2013 

References

1.Benson, D. J., Representations and cohomology, Volume 2: Cohomology of groups and modules (2nd edn), Cambridge Studies in Advanced Mathematics, Volume 31 (Cambridge University Press, 1998).Google Scholar
2.Bestvina, M. and Brady, B., Morse theory and finiteness properties of groups, Invent. Math. 129 (1997), 445–470.CrossRefGoogle Scholar
3.Bieri, R., Homological dimension of discrete groups (2nd edn), Queen Mary College Mathematical Notes (Queen Mary College, London, 1981).Google Scholar
4.Bleak, C. and Lanoe, D., A family of non-isomorphism results, Geom. Dedicata 146 (2010), 21–26.CrossRefGoogle Scholar
5.Brin, M. G., Higher dimensional Thompson groups, Geom. Dedicata 108 (2004), 163–192.CrossRefGoogle Scholar
6.Brin, M. G., Presentations of higher-dimensional Thompson groups, J. Alg. 284 (2005), 520–558.CrossRefGoogle Scholar
7.Brown, K. S., Finiteness properties of groups, J. Pure Appl. Alg. 44 (1987), 45–75.CrossRefGoogle Scholar
8.Burris, S. N. and Sankappanavar, H. P., A course in universal algebra, Graduate Texts in Mathematics, Volume 78 (Springer, 1981).Google Scholar
9.Cohn, P. M., Universal algebra, Mathematics and Its Applications, Volume 6 (D. Reidel, Dordrecht, 1981).Google Scholar
10.Hennig, J. and Matucci, F., Presentations for the higher-dimensional Thompson’s groups nV , Pac. J. Math. 257(1) (2012), 53–74.CrossRefGoogle Scholar
11.Higman, G., Finitely presented infinite simple groups, Notes on Pure Mathematics, Volume 8 (Australian National University, Canberra, 1974).Google Scholar