  We show that a construction by Aanderaa and Cohen used in their proof of the
Higman Embedding Theorem preserves torsion length. We give a new construction
showing that every finitely presented group is the quotient of some $C'(1/6)$
finitely presented group by the subgroup generated by its torsion elements. We
use these results to show there is a finitely presented group with infinite
torsion length which is $C'(1/6)$, and thus word-hyperbolic and virtually
torsion-free.
