On the center of a Coxeter group
| dc.creator | Hosaka, Tetsuya | |
| dc.date | 2005-10-24 | |
| dc.date.accessioned | 2026-07-07T06:47:51Z | |
| dc.date.available | 2026-07-07T06:47:51Z | |
| dc.description | In this paper, we show that the center of every Coxeter group is finite and isomorphic to $(\Z_2)^n$ for some $n\ge 0$. Moreover, for a Coxeter system $(W,S)$, we prove that $Z(W)=Z(W_{S\setminus\tilde{S}})$ and $Z(W_{\tilde{S}})=1$, where $Z(W)$ is the center of the Coxeter group $W$ and $\tilde{S}$ is the subset of $S$ such that the parabolic subgroup $W_{\tilde{S}}$ is the {\it essential parabolic subgroup} of $(W,S)$ (i.e.\ $W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in $(W,S)$). The finiteness of the center of a Coxeter group implies that a splitting theorem holds for Coxeter groups. | |
| dc.identifier | https://arxiv.org/abs/math/0510510 | |
| dc.identifier | http://arxiv.org/abs/math/0510510 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103788 | |
| dc.subject | Group Theory | |
| dc.subject | 20F55 | |
| dc.title | On the center of a Coxeter group | |
| dc.type | text |