Mathematics – Group Theory
Scientific paper
1994-04-22
Mathematics
Group Theory
Plain Tex, 12 pages, no figures
Scientific paper
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''.
Cartwright Donald I.
Shapiro Michael
No associations
LandOfFree
Hyperbolic buildings, affine buildings and automatic groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hyperbolic buildings, affine buildings and automatic groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic buildings, affine buildings and automatic groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-708009