A family of non-isomorphism results |
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Authors: | Collin Bleak Daniel Lanoue |
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Institution: | 1.Department of Mathematics,University of Nebraska,Lincoln,USA;2.Department of Mathematics,University of California at Berkeley,Berkeley,USA |
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Abstract: | We calculate the local groups of germs associated with the higher dimensional R. Thompson groups nV. For a given \({n\in N\cup\left\{\omega\right\}}\) , these groups of germs are free abelian groups of rank r, for r ≤ n (there are some groups of germs associated with nV with rank precisely k for each index 1 ≤ k ≤ n). By Rubin’s theorem, any conjectured isomorphism between higher dimensional R. Thompson groups induces an isomorphism between associated groups of germs. Thus, if m ≠ n the groups mV and nV cannot be isomorphic. This answers a question of Brin. |
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