Fixed points of finite groups acting on generalised Thompson groups
Fixed points of finite groups acting on generalised Thompson groups
We study centralisers of finite order automorphisms of the
generalised Thompson groups Fn, ? and conjugacy classes of finite sub-
groups in finite extensions of Fn, ?. In particular we show that centralisers of finite automorphisms in Fn, ? are either of type FP? or not finitely generated.
As an application we deduce the following result about the Bredon type
of such finite extensions: any finite extension of Fn, ?, where the elements of finite order act on Fn, ? via conjugation with piecewise-linear
homeomorphisms, is of type Bredon F?. In particular finite extensions
of F = F2,? are of type Bredon F?.
167-192
Kochloukova, D.H.
3a54fa65-f950-44b6-beb3-28030dfb2558
Martínez Pérez, C.
59345d63-03cc-4f90-8a55-42bfcb7fa00f
Nucinkis, B.E.A.
41b6a278-1866-4585-84f5-601bb85636a2
2010
Kochloukova, D.H.
3a54fa65-f950-44b6-beb3-28030dfb2558
Martínez Pérez, C.
59345d63-03cc-4f90-8a55-42bfcb7fa00f
Nucinkis, B.E.A.
41b6a278-1866-4585-84f5-601bb85636a2
Kochloukova, D.H., Martínez Pérez, C. and Nucinkis, B.E.A.
(2010)
Fixed points of finite groups acting on generalised Thompson groups.
Israel Journal of Mathematics, 187 (1), .
Abstract
We study centralisers of finite order automorphisms of the
generalised Thompson groups Fn, ? and conjugacy classes of finite sub-
groups in finite extensions of Fn, ?. In particular we show that centralisers of finite automorphisms in Fn, ? are either of type FP? or not finitely generated.
As an application we deduce the following result about the Bredon type
of such finite extensions: any finite extension of Fn, ?, where the elements of finite order act on Fn, ? via conjugation with piecewise-linear
homeomorphisms, is of type Bredon F?. In particular finite extensions
of F = F2,? are of type Bredon F?.
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CentrThompson26-01-10.pdf
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Published date: 2010
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Local EPrints ID: 72179
URI: http://eprints.soton.ac.uk/id/eprint/72179
PURE UUID: ba96089c-509e-421f-ace6-f888f8d11e5a
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Date deposited: 01 Feb 2010
Last modified: 13 Mar 2024 21:06
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Author:
D.H. Kochloukova
Author:
C. Martínez Pérez
Author:
B.E.A. Nucinkis
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