On some integral representations of groups and global irreducibility.
| Autor: | Dmitry Malinin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | International Journal of Group Theory, Vol 7, Iss 3, Pp 81-94 (2018) |
| Druh dokumentu: | article |
| ISSN: | 2251-7650 2251-7669 |
| DOI: | 10.22108/ijgt.2017.100688.1402 |
| Popis: | Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. Let $K$ be a finite extension of the rational number field and $O_K$ the ring of integers of $K$. Let $G$ be a finite subgroup of $GL(2,K)$, the group of $(2 times 2)$-matrices over $K$. We obtain some conditions on $K$ for $G$ to be conjugate to a subgroup of $GL(2,O_K)$. |
| Databáze: | Directory of Open Access Journals |
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