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arXiv · 1403.8060

Free subgroups of special linear groups

Rupert McCallum
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Abstract

We present a proof of the following claim. Suppose that $n$ is an integer such that $n>1$ and that $k$ is any field. Suppose that $g$ is an element of $\mathrm{SL}(n,k)$ of infinite order. Then the set $\{h\in\mathrm{SL}(n,k)\mid $ is a free group of rank two$\}$ is a Zariski dense subset of $\mathrm{SL}(n,\bar{k})$ where $\bar{k}$ is an algebraic closure of $k$.

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Rupert McCallum. 2014-03-31. Free subgroups of special linear groups. https://arxiv.org/abs/1403.8060

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