Torsion, torsion length and finitely presented groups

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 C⁰.1=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 C⁰.1=6/, and thus word-hyperbolic and virtually torsion-free.