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Finiteness Properties of Some Groups of Local Similarities

Published online by Cambridge University Press:  10 April 2015

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])

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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