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dc.contributor.authorBleak, Collin Patrick
dc.contributor.authorSalazar-Diaz, Olga
dc.identifier.citationBleak , 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 .
dc.identifier.otherPURE: 5347678
dc.identifier.otherPURE UUID: 8f570ce6-bd98-4372-97df-05b10aa04fa8
dc.identifier.otherScopus: 84882657273
dc.identifier.otherORCID: /0000-0001-5790-1940/work/73701272
dc.description.abstractWe 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.
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.rights© Copyright 2013 American Mathematical Society. First published in Transactions of the American Mathematical Society in volume 365 2013, published by the American Mathematical Societyen
dc.subjectR. Thompson Groupsen
dc.subjectCantor Seten
dc.subjectQA Mathematicsen
dc.titleFree products in R. Thompson’s group Ven
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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