Reflections in abstract Coxeter groups
| dc.creator | Franzsen, W. N. | |
| dc.creator | Howlett, R. B. | |
| dc.creator | Mühlherr, B. | |
| dc.date | 2005-06-28 | |
| dc.date.accessioned | 2026-07-07T05:21:12Z | |
| dc.date.available | 2026-07-07T05:21:12Z | |
| dc.description | Let $W$ be a Coxeter group and $r\in W$ a reflection. If the group of order 2 generated by $r$ is the intersection of all the maximal finite subgroups of $W$ that contain it, then any isomorphism from $W$ to a Coxeter group $W'$ must take $r$ to a reflection in $W'$. The aim of this paper is to show how to determine, by inspection of the Coxeter graph, the intersection of the maximal finite sugroups containing $r$. In particular we show that the condition above is satisfied whenever $W$ is infinite and irreducible, and has the property that all rank two parabolic subgroups are finite. So in this case all isomorphisms map reflections to reflections. | |
| dc.description | 25 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/math/0506573 | |
| dc.identifier | http://arxiv.org/abs/math/0506573 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75604 | |
| dc.subject | Group Theory | |
| dc.subject | 20F55 (primary), 51F55(secondary) | |
| dc.title | Reflections in abstract Coxeter groups | |
| dc.type | text |