On finite linear groups stable under Galois operation

Ekaterina Khrebtova, Dmitry Malinin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a Galois extension E/F of characteristic 0 and realization fields of finite abelian subgroups G ⊂ GLn(E) of a given exponent t. We 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)17-27
Number of pages11
JournalActa Mathematica Academiae Paedagogicae Nyiregyhaziensis
Volume25
Issue number1
Publication statusPublished - 2009

Keywords

  • Algebraic integers
  • Galois algebras
  • Galois group
  • Integral representations

ASJC Scopus subject areas

  • General Mathematics
  • Education

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