On some integral representations of groups and global irreducibility.
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 rin...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2018-09-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf |
| _version_ | 1818960257958805504 |
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| author | Dmitry Malinin |
| author_facet | Dmitry Malinin |
| author_sort | Dmitry Malinin |
| collection | DOAJ |
| description | 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 $GL(2,O_K)$. |
| first_indexed | 2024-12-20T11:54:40Z |
| format | Article |
| id | doaj.art-02a3520ae05448fd97b1c2d16a386e30 |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-12-20T11:54:40Z |
| publishDate | 2018-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-02a3520ae05448fd97b1c2d16a386e302022-12-21T19:41:40ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692018-09-0173819410.22108/ijgt.2017.100688.140222289On some integral representations of groups and global irreducibility.Dmitry Malinin0UWI, Mona, KingstonArithmetic 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 $GL(2,O_K)$.http://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdfglobally irreducible representationsclass numbersgeneraHilbert symboltorsion points of elliptic curves |
| spellingShingle | Dmitry Malinin On some integral representations of groups and global irreducibility. International Journal of Group Theory globally irreducible representations class numbers genera Hilbert symbol torsion points of elliptic curves |
| title | On some integral representations of groups and global irreducibility. |
| title_full | On some integral representations of groups and global irreducibility. |
| title_fullStr | On some integral representations of groups and global irreducibility. |
| title_full_unstemmed | On some integral representations of groups and global irreducibility. |
| title_short | On some integral representations of groups and global irreducibility. |
| title_sort | on some integral representations of groups and global irreducibility |
| topic | globally irreducible representations class numbers genera Hilbert symbol torsion points of elliptic curves |
| url | http://ijgt.ui.ac.ir/article_22289_b241fb85a1db50082f5c3c1e8b74e634.pdf |
| work_keys_str_mv | AT dmitrymalinin onsomeintegralrepresentationsofgroupsandglobalirreducibility |