The loop of rope with a running knot used to hang a person

One word substitute is Noose.

Noose: a loop with a running knot, tightening as the rope or wire is pulled and used to trap animals or hang people.
Cable: a thick rope of wire or hemp used for construction, mooring ships, and towing vehicles.
Cord: thin, flexible string or rope made from several twisted strands.
Chord: a group of (typically three or more) notes sounded together, as a basis of harmony.