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Free products in R. Thompson’s group V

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Bleak_2013_TAMS_Free.pdf (332.8Kb)
Date
11/2013
Author
Bleak, Collin Patrick
Salazar-Diaz, Olga
Keywords
R. Thompson Groups
Homeomorphisms
Cantor Set
QA Mathematics
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Abstract
We investigate some product structures in R. Thompson's group $ V$, primarily by studying the topological dynamics associated with $ V$'s action on the Cantor set C. We draw attention to the class D(V,C) of groups which have embeddings as demonstrative subgroups of V whose class can be used to assist in forming various products. Note that D(V,C) contains all finite groups, the free group on two generators, and Q/Z, and is closed under passing to subgroups and under taking direct products of any member by any finite member. If G≤V and H ∈ D(V,C), then G~H embeds into V. Finally, if G, H ∈ D(V,C), then G*H embeds in V. Using a dynamical approach, we also show the perhaps surprising result that Z2 * Z does not embed in V, even though V has many embedded copies of Z2 and has many embedded copies of free products of various pairs of its subgroups.
Citation
Bleak , C P & Salazar-Diaz , O 2013 , ' Free products in R. Thompson’s group V ' , Transactions of the American Mathematical Society , vol. 365 , no. 11 , pp. 5967-5997 . https://doi.org/10.1090/S0002-9947-2013-05823-0
Publication
Transactions of the American Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1090/S0002-9947-2013-05823-0
ISSN
0002-9947
Type
Journal article
Rights
© Copyright 2013 American Mathematical Society. First published in Transactions of the American Mathematical Society in volume 365 2013, published by the American Mathematical Society
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/5237

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