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Free subgroups of special linear groups

Authors :
McCallum, Rupert
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Comment: This paper has been withdrawn by the author due to an error in the proof of Lemma 8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

Subjects :
Mathematics - Group Theory
20G15

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1403.8060
Document Type :
Working Paper