text: abstract. 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.