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 journalArticlepeer-review


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 languageEnglish
Pages (from-to)827-840
Number of pages14
JournalBulletin of the Malaysian Mathematical Sciences Society
Issue number2
Publication statusPublished - Apr 2015
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Representations of some groups and Galois stability'. Together they form a unique fingerprint.

Cite this