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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!
Shlomi.

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.

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    $\begingroup$ Why don't you ask Schupp? Here is his webpage: math.uiuc.edu/People/schupp.html $\endgroup$
    – Sam Nead
    Jan 27, 2015 at 21:15
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    $\begingroup$ [Too long for a comment] No mathematical content to offer, but the name is almost certainly a reference to the Indian Rope Trick (see en.wikipedia.org/wiki/Indian_rope_trick), which is a famous magic trick in which a boy climbs up a rope and disappears. Perhaps the lemma has something to do with "climbing up" and "vanishing"; perhaps they just thought the word "Higman" sounded a little bit like the word "Indian" (they both end in "an") and made a little joke instead of just calling it the Higman Trick? $\endgroup$
    – Flounderer
    Jan 27, 2015 at 21:18
  • $\begingroup$ well, the "rope trick" refers to a rope which is supported from the wrong direction; the theorem referred to is given at the end of Higman's paper, supporting the whole argument "from the wrong direction" $\endgroup$
    – Carlo Beenakker
    Jan 27, 2015 at 21:18
  • $\begingroup$ @Flounderer You're move than welcome to turn your comment into an answer and have it accepted. $\endgroup$
    – ShlomiF
    Jan 28, 2015 at 23:46
  • $\begingroup$ @ShlomiF Thanks! I am glad you got your answer. I did originally post the answer as an answer but was instructed to turn it into a comment. I have now turned the comment into an answer. $\endgroup$
    – Flounderer
    Jan 29, 2015 at 1:23

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[Too long for a comment] No mathematical content to offer, but the name is almost certainly a reference to the Indian Rope Trick (see http://en.wikipedia.org/wiki/Indian_rope_trick), which is a famous magic trick in which a boy climbs up a rope and disappears. Perhaps the lemma has something to do with "climbing up" and "vanishing"; perhaps they just thought the word "Higman" sounded a little bit like the word "Indian" (they both end in "an") and made a little joke instead of just calling it the Higman Trick?

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  • $\begingroup$ Next time, break this up into two comments. Gerhard "You Will Be Forgiven Faster" Paseman, 2015.01.27 $\endgroup$
    – Gerhard Paseman
    Jan 27, 2015 at 20:54
  • $\begingroup$ I am happy to delete it if you are prepared to forgive me. $\endgroup$
    – Flounderer
    Jan 27, 2015 at 20:59
  • $\begingroup$ OK. Gerhard "Go, And Sin No More" Paseman, 2015.01.27 $\endgroup$
    – Gerhard Paseman
    Jan 27, 2015 at 21:05
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Well, Sam Nead and Flounderer got it right but in different ways... :-)
I took up Sam's idea and asked Schupp directly.
He said Flounderer was right, and I'll quote:
"The answer on mathoverflow is exactly correct - the reference is to the Indian Rope Trick. I always think of the lemma in the following way: As one is concentrating on the details of the proof, Higman the magician makes the infinitely many relations disappear. The Higman Embedding Theorem is certainly one of the great theorems."
So all credit to Schupp and Flounderer, but I decided to post this as an answer for the sake of closure. Thanx all,
Shlomi.

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