Coxeter covers of the symmetric groups
| dc.creator | Rowen, Louis H. | |
| dc.creator | Teicher, Mina | |
| dc.creator | Vishne, Uzi | |
| dc.date | 2004-05-11 | |
| dc.date.accessioned | 2026-07-07T05:08:07Z | |
| dc.date.available | 2026-07-07T05:08:07Z | |
| dc.description | We study Coxeter groups from which there is a natural map onto a symmetric group. Such groups have natural quotient groups related to presentations of the symmetric group on an arbitrary set $T$ of transpositions. These quotients, denoted here by C_Y(T), are a special type of the generalized Coxeter groups defined in \cite{CST}, and also arise in the computation of certain invariants of surfaces. We use a surprising action of $S_n$ on the kernel of the surjection $C_Y(T) \ra S_n$ to show that this kernel embeds in the direct product of $n$ copies of the free group $π_1(T)$ (with the exception of $T$ being the full set of transpositions in $S_4$). As a result, we show that the groups $C_Y(T)$ are either virtually Abelian or contain a non-Abelian free subgroup. | |
| dc.description | 32 pp. Accepted to Journal of Group Theory | |
| dc.identifier | https://arxiv.org/abs/math/0405185 | |
| dc.identifier | http://arxiv.org/abs/math/0405185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71131 | |
| dc.subject | Group Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Coxeter covers of the symmetric groups | |
| dc.type | text |