Representations of some groups and Galois stability

Dmitry Malinin; Nor Haniza Sarmin; Nor Muhainiah Mohd Ali; Zainab Yahya; Noor Asma’ Adny Mohd Adnan

doi:10.1007/s40840-014-0051-7

Representations of some groups and Galois stability

Dmitry Malinin, Nor Haniza Sarmin, Nor Muhainiah Mohd Ali, Zainab Yahya, Noor Asma’ Adny Mohd Adnan

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	827-840
Number of pages	14
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/s40840-014-0051-7
Publication status	Published - Apr 2015
Externally published	Yes

Keywords

Algebraic integers
Galois groups
Integral representations
Permutation modules and lattices
Realization fields

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s40840-014-0051-7

Cite this

@article{2e970a8353a04665ba343b42fbb65f58,

title = "Representations of some groups and Galois stability",

abstract = "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.",

keywords = "Algebraic integers, Galois groups, Integral representations, Permutation modules and lattices, Realization fields",

author = "Dmitry Malinin and Sarmin, {Nor Haniza} and {Mohd Ali}, {Nor Muhainiah} and Zainab Yahya and {Mohd Adnan}, {Noor Asma{\textquoteright} Adny}",

note = "Publisher Copyright: {\textcopyright} Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2014.",

year = "2015",

month = apr,

doi = "10.1007/s40840-014-0051-7",

language = "English",

volume = "38",

pages = "827--840",

journal = "Bulletin of the Malaysian Mathematical Sciences Society",

issn = "0126-6705",

publisher = "Springer Science+Business Media Singapore Private Limited",

number = "2",

}

TY - JOUR

T1 - Representations of some groups and Galois stability

AU - Malinin, Dmitry

AU - Sarmin, Nor Haniza

AU - Mohd Ali, Nor Muhainiah

AU - Yahya, Zainab

AU - Mohd Adnan, Noor Asma’ Adny

N1 - Publisher Copyright: © Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2014.

PY - 2015/4

Y1 - 2015/4

N2 - 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.

AB - 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.

KW - Algebraic integers

KW - Galois groups

KW - Integral representations

KW - Permutation modules and lattices

KW - Realization fields

UR - http://www.scopus.com/inward/record.url?scp=84925857069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925857069&partnerID=8YFLogxK

U2 - 10.1007/s40840-014-0051-7

DO - 10.1007/s40840-014-0051-7

M3 - Article

AN - SCOPUS:84925857069

SN - 0126-6705

VL - 38

SP - 827

EP - 840

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 2

ER -

Representations of some groups and Galois stability

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this