On finite linear groups stable under Galois operation

Khrebtova, Ekaterina and Malinin, Dmitry (2009) On finite linear groups stable under Galois operation. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 25 (1). pp. 17-27. ISSN 0866-0174

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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

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