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Embedding And Nonembedding Results For R. Thompson's Group V And Related Groups, Nathan Corwin

Department of Mathematics: Dissertations, Theses, and Student Research

We study Richard Thompson's group V, and some generalizations of this group. V was one of the first two examples of a finitely presented, infinite, simple group. Since being discovered in 1965, V has appeared in a wide range of mathematical subjects. Despite many years of study, much of the structure of V remains unclear. Part of the difficulty is that the standard presentation for V is complicated, hence most algebraic techniques have yet to prove fruitful.

This thesis obtains some further understanding of the structure of V by showing the nonexistence of the wreath product Z wr Z^2 as …