A family of non-isomorphism results
Open Access Publications from the University of California

## A family of non-isomorphism results

• Author(s): Bleak, Collin;
• Lanoue, Daniel
• et al.

## Published Web Location

https://doi.org/10.1007/s10711-009-9423-9
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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