The Galois group of random elements of linear groups

Alexander Lubotzky; Lior Rosenzweig

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arXiv · 1205.5290

The Galois group of random elements of linear groups

Alexander Lubotzky·Lior Rosenzweig

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Abstract

Let F be a finitely generated field of characteristic zero and \Gamma<GL_n(F) a finitely generated subgroup. For an element g in \Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over F. We show that the structure of Gal(F(g)/ F) has a typical behaviour depending on F, and on the geometry of the Zariski closure of \Gamma (but not on \Gamma).

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Alexander Lubotzky, Lior Rosenzweig. 2012-05-23. The Galois group of random elements of linear groups. https://arxiv.org/abs/1205.5290

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