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Finiteness Properties of Some Groups of Local Similarities

Part of: Spaces with richer structures Special aspects of infinite or finite groups Locally compact groups and their algebras

Published online by Cambridge University Press:  10 April 2015

Daniel S. Farley  and
Bruce Hughes
Daniel S. Farley
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USA, ([email protected])
Bruce Hughes
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA, ([email protected])
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Abstract

Hughes has defined a class of groups that we call finite similarity structure (FSS) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson’s group V. Guided by previous work on Thompson’s group, we show that many FSS groups are of type F∞. This generalizes work of Ken Brown from the 1980s.

Keywords

finite similarity structureNekrashevych–Röver groupsThompson’s grouptype F∞ultrametriczipper action

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 22D10: Unitary representations of locally compact groups 54E45: Compact (locally compact) metric spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 379 - 402
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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References

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