The computational complexity of torsion-freeness of finitely presented groups
Steffen Lempp · Bulletin of the Australian Mathematical Society · 1997
We determine the complexity of torsion-freeness of finitely presented groups in Kleene's arithmetical hierarchy as -complete. This implies in particular that there is no effective listing of all torsion-free finitely presented groups, or of all non-torsion-free finitely presented groups.