  We give a complete survey of a construction by Boone and Collins for
embedding any finitely presented group into one with $8$ generators and $26$
relations. We show that this embedding preserves the set of orders of torsion
elements, and in particular torsion-freeness. We combine this with the
independent results of Belegradek and Chiodo to prove that there is an
$8$-generator $26$-relator universal finitely presented torsion-free group (one
into which all finitely presented torsion-free groups embed).
