## Infinite generation of non-cocompact lattices on right-angled buildings

### Anne Thomas and Kevin Wortman

#### Abstract

Let $\Gamma$ be a non-cocompact lattice on a locally finite regular right-angled building $X$. We prove that if $\Gamma$ has a strict fundamental domain then $\Gamma$ is not finitely generated. We use the separation properties of subcomplexes of $X$ called tree-walls.

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 Wednesday, September 22, 2010