On symmetric units in group algebras
| dc.creator | Bovdi, Victor | |
| dc.date | 2000-09-01 | |
| dc.date.accessioned | 2026-07-07T04:37:06Z | |
| dc.date.available | 2026-07-07T04:37:06Z | |
| dc.description | Let $U(KG)$ be the group of units of the group ring $KG$ of the group $G$ over a commutative ring $K$. The anti-automorphism $g\mapsto g\m1$ of $G$ can be extended linearly to an anti-automorphism $a\mapsto a^*$ of $KG$. Let $S_*(KG)=\{x\in U(KG) \mid x^*=x\}$ be the set of all symmetric units of $U(KG)$. We consider the following question: for which groups $G$ and commutative rings $K$ it is true that $S_*(KG)$ is a subgroup in $U(KG)$. We answer this question when either a) $G$ is torsion and $K$ is a commutative $G$-favourable integral domain of characteristic $p\geq 0$ or b) $G$ is non-torsion nilpotent group and $KG$ is semiprime. | |
| dc.description | 11 pages, AMS-TeX, to appear in Comm. in Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0009006 | |
| dc.identifier | http://arxiv.org/abs/math/0009006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59835 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Group Theory | |
| dc.subject | 20C05, 20C07, 16S34 | |
| dc.title | On symmetric units in group algebras | |
| dc.type | text |