Nylon rope, especially, is usually whipped by fusing the end in a nice black blob.
I'm not sure I would do that. The charred nylon can be quite hard (Geoffrey Budworth relayed a story of a tugboat captain that got his hand sliced opened up by the fused end of a rope). And, burning nylon can release some very unpleasant gasses. If you're dead set on making the end of the rope rigid, soak it in 1/1 diluted waterproof PVA glue. I'm partial to Elmer's Craft-bond Fabric and Paper if appearance matters or Titebond II if I can tolerate the yellowing.