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arXiv · 2611.03175

Constructing free subgroups of matrix groups

Emmanuel Breuillard·Bettina Eick·Tommy Hofmann·Derek Holt·Eamonn O'Brien
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Abstract

The Tits alternative asserts that a finitely generated linear group is either solvable-by-finite or contains a non-abelian free subgroup. Given a non-solvable-by-finite subgroup G of GL(d, F), where F is the field of complex numbers or a non-archimedean local field, we present methods to construct explicitly a non-abelian 2-generator free subgroup of G in specific cases. Our implementations in the computeralgebra system Oscar are publicly available.

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Emmanuel Breuillard, Bettina Eick, Tommy Hofmann, Derek Holt, Eamonn O'Brien. 2026-11-02. Constructing free subgroups of matrix groups. https://arxiv.org/abs/2611.03175

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