Representations of some groups and galois stability
We study arithmetic problems for representations of finite groups over algebraic number fields and their orders under the ground field extensions. Let E/F be a Galois extension, and let G ? GL n (E) be a subgroup stable under the natural operation of the Galois group of E/F. A concept generalizing p...
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| Main Authors: | , , , , |
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| Format: | Article |
| Published: |
Springer Science+Business Media Singapore Private Limited
2015
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/54621/ http://dx.doi.org/10.1007/s40840-014-0051-7 |
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| Institution: | Universiti Teknologi Malaysia |
| Summary: | We study arithmetic problems for representations of finite groups over algebraic number fields and their orders under the ground field extensions. Let E/F be a Galois extension, and let G ? GL n (E) be a subgroup stable under the natural operation of the Galois group of E/F. A concept generalizing permutation modules is used to determine the structure of groups G and their realization fields. We also compare the possible realization fields of G in the cases if G ? GL n (E), and if all coeffi-cients of matrices in G are algebraic integers. Some related results and conjectures are considered. |
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