The Galois group of random elements of linear groups

Alexander Lubotzky*, Lior Rosenzweig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let 𝔽 be a finitely generated field of characteristic zero and Γ ≤ GLn(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 languageEnglish
Pages (from-to)1347-1383
Number of pages37
JournalAmerican Journal of Mathematics
Volume136
Issue number5
DOIs
StatePublished - 1 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014 by Johns Hopkins University Press.

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