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Free subgroups of special linear groups
- Publication Year :
- 2014
-
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 $\{h\in\mathrm{SL}(n,k)\mid <g,h>$ 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 $k$.<br />Comment: This paper has been withdrawn by the author due to an error in the proof of Lemma 8
- Subjects :
- Mathematics - Group Theory
20G15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1403.8060
- Document Type :
- Working Paper