Isomorphisms between centers of integral group rings
| dc.creator | Hertweck, Martin | |
| dc.date | 2006-12-15 | |
| dc.date.accessioned | 2026-07-07T07:35:22Z | |
| dc.date.available | 2026-07-07T07:35:22Z | |
| dc.description | For finite nilpotent groups $G$ and $G^{\prime}$, and a $G$-adapted ring $S$ (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings $SG$ and $SG^{\prime}$ is monomial, i.e., maps class sums in $SG$ to class sums in $SG^{\prime}$ up to multiplication with roots of unity. As a consequence, $G$ and $G^{\prime}$ have identical character tables if and only if the centers of their integral group rings $\mathbb{Z} G$ and $\mathbb{Z} G^{\prime}$ are isomorphic. In the course of the proof, a new proof of the class sum correspondence is given. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612436 | |
| dc.identifier | http://arxiv.org/abs/math/0612436 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120069 | |
| dc.subject | Representation Theory | |
| dc.subject | Group Theory | |
| dc.subject | 20C05, 20C15 (Primary) 13F99 (Secondary) | |
| dc.title | Isomorphisms between centers of integral group rings | |
| dc.type | text |