I'm studiyng Higman's Embedding Theorem, and a fundamental part of the proof is the following lemma:
If R is a benign normal subgroup of finitely generated group F, then F/R can be embedded in a finitely presented group.
A proof of the lemma in context could be found on page 16 of this paper.
I understand the lemma on technical levels, and to some degree also on an intuitive level.
But I have no idea why Lyndon & Schupp chose the name "The Higman Rope Trick" for the lemma.
I'm hoping someone could enlighten me because my feeling is that I'm missing something important about the meaning of the lemma...otherwise I'd get the meaning of the name, not so?
Thank you very much!
P.S: This is my first time posting a question. I read the different guides and I'm pretty sure I stuck to the rules. If not though then I apologize and will correct upon notice.