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- W2040783000 abstract "We see that a building whose Coxeter group is hyperbolic is itself hyperbolic. Thus any finitely generated group acting co-compactly on such a building is hyperbolic, hence automatic. We turn our attention to affine buildings and consider a group $Gamma$ which acts simply transitively and in a ``type-rotating'' way on the vertices of a locally finite thick building of type $tilde A_n$. We show that $Gamma$ is biautomatic, using a presentation of $Gamma$ and unique normal form for each element of $Gamma$, as described in ``Groups acting simply transitively on the vertices of a building of type $tilde A_n$'' by D.I. Cartwright, to appear, Proceedings of the 1993 Como conference ``Groups of Lie type and their geometries''." @default.
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- W2040783000 date "1995-01-01" @default.
- W2040783000 modified "2023-09-25" @default.
- W2040783000 title "Hyperbolic buildings, affine buildings, and automatic groups." @default.
- W2040783000 doi "https://doi.org/10.1307/mmj/1029005309" @default.
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