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arXiv:1205.5290 [math.NT]AbstractReferencesReviewsResources

The Galois group of random elements of linear groups

Alexander Lubotzky, Lior Rosenzweig

Published 2012-05-23Version 1

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).

Categories: math.NT, math.GR, math.RT
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