We define a family of groups that generalises Thompson’s groups and , and also those of Higman, Stein and Brin. For groups in this family we describe centralisers of finite subgroups and show that for a given finite subgroup there are finitely many conjugacy classes of finite subgroups isomorphic to . We consider groups of type quasi-. This is a property slightly weaker than possessing a finite type model for the classifying space for proper actions . We give criteria for the versions of our groups to be of type quasi-. We also generalise some well-known properties of ordinary cohomology to Bredon cohomology.
Cite this article
Conchita Martínez-Pérez, Brita E. A. Nucinkis, Bredon cohomological finiteness conditions for generalisations of Thompson groups. Groups Geom. Dyn. 7 (2013), no. 4, pp. 931–959DOI 10.4171/GGD/211