Orders generated by character values
| Autor: | Bächle, Andreas, Sambale, Benjamin |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Monatsh. Math. 191, 665-678 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00605-019-01324-3 |
| Popis: | Let $K:=\mathbb{Q}(G)$ be the number field generated by the complex character values of a finite group $G$. Let $\mathbb{Z}_K$ be the ring of integers of $K$. In this paper we investigate the suborder $\mathbb{Z}[G]$ of $\mathbb{Z}_K$ generated by the character values of $G$. We prove that every prime divisor of the order of the finite abelian group $\mathbb{Z}_K/\mathbb{Z}[G]$ divides $|G|$. Moreover, if $G$ is nilpotent, we show that the exponent of $\mathbb{Z}_K/\mathbb{Z}[G]$ is a proper divisor of $|G|$ unless $G=1$. We conjecture that this holds for arbitrary finite groups $G$. Comment: 12 pages. To appear in Monatsh. Math |
| Databáze: | arXiv |
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