On some applications of finite galois stable linear groups

Ekaterina Khrebtova, Dmitry Malinin

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We consider a Galois extensions E/F and realization fields of finite abelian subgroups G ⊂ GL n(E) of a given exponent t. Let us assume that G is stable under the natural operation of the Galois group of E=F. It is proven that under some reasonable restrictions for n any E can be a realization field of G, while if all coefficients of matrices in G are algebraic integers there are only finitely many fields E of realization having a given degree d for prescribed integers n and t or prescribed n and d: Some related results and conjectures are considered.

Original languageEnglish
Pages (from-to)1133-1141
Number of pages9
JournalWorld Academy of Science, Engineering and Technology
Publication statusPublished - Jan 2009
Externally publishedYes


  • Algebraic integers
  • Galois groups
  • Integral representations
  • Realization fields

ASJC Scopus subject areas

  • General Engineering

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