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Torsion-freeness problem for matrix groups
We establish three results on decision problems for finitely generated matrix groups, based on fiber products: $\bullet$ The torsion-freeness problem is undecidable for subgroups of $\mathrm{SL}_{4}(\mathbb{Z})$, $\bullet$ There exists a finitely generated subgroup $G$ of $\mathrm{SL}_{4}(\mathb
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