Coxeter covers of the classical Coxeter groups
| dc.creator | Amram, M. | |
| dc.creator | Shwartz, R. | |
| dc.creator | Teicher, M. | |
| dc.date | 2008-03-20 | |
| dc.date.accessioned | 2026-07-07T09:27:39Z | |
| dc.date.available | 2026-07-07T09:27:39Z | |
| dc.description | Let $C(T)$ be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either $B_n$ or $D_n$. Let $C_Y(T)$ be a natural quotient of $C(T)$, and if $C(T)$ is simply-laced (which means all the relations between the generators has order 2 or 3), $C_Y(T)$ is a generalized Coxeter group, too . Let $A_{t,n}$ be a group which contains $t$ Abelian groups generated by $n$ elements. The main result in this paper is that $C_Y(T)$ is isomorphic to $A_{t,n} \semidirect B_n$ or $A_{t,n} \semidirect D_n$, depends on whether the signed graph $T$ contains loops or not, or in other words C(T) is simply-laced or not, and $t$ is the number of the cycles in $T$. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups. | |
| dc.description | 26 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/0803.3010 | |
| dc.identifier | http://arxiv.org/abs/0803.3010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157182 | |
| dc.subject | Group Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 20B30, 20E34, 20F05, 20F55, 20F65 | |
| dc.title | Coxeter covers of the classical Coxeter groups | |
| dc.type | text |