Free products in R. Thompson’s group V
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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.
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
Transactions of the American Mathematical Society
© Copyright 2013 American Mathematical Society. First published in Transactions of the American Mathematical Society in volume 365 2013, published by the American Mathematical Society