Fixed points of finite groups acting on generalised Thompson groups

D. H. Kochloukova; C. Martínez-Pérez; B. E. A. Nucinkis

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arXiv · 1002.1866

Fixed points of finite groups acting on generalised Thompson groups

D. H. Kochloukova·C. Martínez-Pérez·B. E. A. Nucinkis

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Abstract

We study centralisers of finite order automorphisms of generalisations of Thompson's group F and conjugacy classes of finite subgroups in finite extensions of these groups. In particular, we show that centralisers of finite automorphisms in these generalised Thompson groups either admit a finite type classifying space or are not finitely generated. As an application we deduce results about the Bredon type of such finite extensions.

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D. H. Kochloukova, C. Martínez-Pérez, B. E. A. Nucinkis. 2010-02-09. Fixed points of finite groups acting on generalised Thompson groups. https://arxiv.org/abs/1002.1866

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