If so, is there a way to conclude this from Malcev's theorem?
In general, what is known about virtually torsion freeness of non-finitely generated linear groups?
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$\begingroup$ If you take an open subgroup of the form $U=SL_n(p^m {\mathbb Z}_p)$ (congruence subgroup of level $p^m$ ) then the log map on this is an isomorphism onto the image. In particular, if $g\in U$ such that $g^k=1$ then $klog (g)=0$ whence $log g=0$ hence $g=1$; that is, $U$ is torsion-free. $\endgroup$– VenkataramanaCommented Mar 24, 2017 at 14:08
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$SL_n(\mathbb{Z}_p)$ is virtually torsion free as it is $p$-adic analytic and therefore contains a uniformly powerful open subgroup.
answered Mar 19, 2017 at 21:33