#### Volume 11, issue 2 (2011)

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

### Anne Thomas and Kevin Wortman

Algebraic & Geometric Topology 11 (2011) 929–938
##### 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.

##### Keywords
finite generation, lattice, building
##### Mathematical Subject Classification 2010
Primary: 20E42, 20F05
Secondary: 20F55, 57M07, 51E24