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arXiv · 2212.08114

Strongly dense free subgroups of semisimple algebraic groups II

Emmanuel Breuillard·Robert Guralnick·Michael Larsen
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Abstract

It was shown in Part I that there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski-dense. Here we show that the same is true for as long as the transcendence degree of the field is at least $1$ in characteristic zero and at least $2$ in positive characteristic. We also consider related questions for surface groups.

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Emmanuel Breuillard, Robert Guralnick, Michael Larsen. 2022-12-15. Strongly dense free subgroups of semisimple algebraic groups II. https://arxiv.org/abs/2212.08114

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