THE GALOIS GROUP OF RANDOM ELEMENTS OF LINEAR GROUPS

被引：4

作者：

Lubotzky, Alexander ^{[1
]}

Rosenzweig, Lior ^{[2
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

[2] KTH Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2014年 / 136卷 / 05期

关键词：

SPLITTING FIELDS; POLYNOMIALS; SUBGROUPS;

D O I：

10.1353/ajm.2014.0038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F be a finitely generated field of characteristic zero and Gamma <= GL(n) (F) a finitely generated subgroup. For gamma is an element of Gamma, let Gal(F(gamma)/F) be the Galois group of the splitting field of the characteristic polynomial of gamma over F. We show that the structure of Gal(F(gamma)/F) has a typical behavior depending on F, and on the geometry of the Zariski closure off Gamma (but not on Gamma).

引用

页码：1347 / 1383

页数：37

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