The Galois group of random elements of linear groups

Alexander Lubotzky; Lior Rosenzweig

doi:10.1353/ajm.2014.0038

The Galois group of random elements of linear groups

Alexander Lubotzky^*
, Lior Rosenzweig

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let 𝔽 be a finitely generated field of characteristic zero and Γ ≤ GL_n(𝔽) a finitely generated subgroup. For γ ∈ Γ, let Gal(𝔽(γ)/𝔽) be the Galois group of the splitting field of the characteristic polynomial of γ over 𝔽. We show that the structure of Gal(𝔽(γ)/𝔽) has a typical behavior depending on 𝔽, and on the geometry of the Zariski closure of Γ (but not on Γ).

Original language	English
Pages (from-to)	1347-1383
Number of pages	37
Journal	American Journal of Mathematics
Volume	136
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2014.0038
State	Published - 1 Oct 2014

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© 2014 by Johns Hopkins University Press.

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The Galois group of random elements of linear groups

Abstract

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