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
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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 -