Acta Mathematica Academiae Paedagogicae NyÃregyháziensis | |
On finite linear groups stable under Galois operation | |
Dmitry Malinin1  Ekaterina Khrebtova1  | |
[1] Avango International, UAE and Belarusian National Technical University | |
关键词: Galois algebras; | |
DOI : | |
学科分类:数学(综合) | |
来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica | |
【 摘 要 】
We consider a Galois extension $E/F$ of characteristic 0 and realization fields of finite abelian subgroups $Gsubset GL_n(E)$ 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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912020427694ZK.pdf | 203KB | download |