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arXiv · 1707.02508

Generic elements of a Zariski-dense subgroup form an open subset

Gopal Prasad·Andrei S. Rapinchuk
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Abstract

Let G be a semi-simple algebraic group over a finitely generated field K of characteristic zero, and let \Gamma < G(K) be a finitely generated Zariski-dense subgroup. In this note we prove that the set of K-generic elements of \Gamma (whose existence was established earlier in [9]) is open in the profinite topology of \Gamma. We then extend this result to the fields of positive characteristic, and also prove the existence of generic elements in this case.

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Gopal Prasad, Andrei S. Rapinchuk. 2017-07-09. Generic elements of a Zariski-dense subgroup form an open subset. https://arxiv.org/abs/1707.02508

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