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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: Malinin, Dmitry A., Sarmin, Nor Haniza, Mohd. Ali, Nor Muhainiah, Yahya, Zainab, Mohd. Adnan, Noor Asma’ Adny
Format: Article
Published: Springer Science+Business Media Singapore Private Limited 2015
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QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/54621/
http://dx.doi.org/10.1007/s40840-014-0051-7
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spelling my.utm.546212016-08-24T04:32:57Z http://eprints.utm.my/id/eprint/54621/ Representations of some groups and galois stability Malinin, Dmitry A. Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Yahya, Zainab Mohd. Adnan, Noor Asma’ Adny QA Mathematics 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. Springer Science+Business Media Singapore Private Limited 2015 Article PeerReviewed Malinin, Dmitry A. and Sarmin, Nor Haniza and Mohd. Ali, Nor Muhainiah and Yahya, Zainab and Mohd. Adnan, Noor Asma’ Adny (2015) Representations of some groups and galois stability. Bulletin of the Malaysian Mathematical Sciences Society, 38 (2). pp. 827-840. ISSN 0126-6705 http://dx.doi.org/10.1007/s40840-014-0051-7 DOI:10.1007/s40840-014-0051-7
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Malinin, Dmitry A.
Sarmin, Nor Haniza
Mohd. Ali, Nor Muhainiah
Yahya, Zainab
Mohd. Adnan, Noor Asma’ Adny
Representations of some groups and galois stability
description 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.
format Article
author Malinin, Dmitry A.
Sarmin, Nor Haniza
Mohd. Ali, Nor Muhainiah
Yahya, Zainab
Mohd. Adnan, Noor Asma’ Adny
author_facet Malinin, Dmitry A.
Sarmin, Nor Haniza
Mohd. Ali, Nor Muhainiah
Yahya, Zainab
Mohd. Adnan, Noor Asma’ Adny
author_sort Malinin, Dmitry A.
title Representations of some groups and galois stability
title_short Representations of some groups and galois stability
title_full Representations of some groups and galois stability
title_fullStr Representations of some groups and galois stability
title_full_unstemmed Representations of some groups and galois stability
title_sort representations of some groups and galois stability
publisher Springer Science+Business Media Singapore Private Limited
publishDate 2015
url http://eprints.utm.my/id/eprint/54621/
http://dx.doi.org/10.1007/s40840-014-0051-7
_version_ 1643653556853538816
score 13.188404

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