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Shaun
Shaun
21:46
The following answer of mine was downvoted. I'm not sure why.
-1
A: Do elements $x^2$ and $y$ commute in group $G = \langle x,y \mid x^4, y^{10}, xyx^{-1}y^{-3} \rangle?$

ShaunNo. gap> F:=FreeGroup(2); <free group on the generators [ f1, f2 ]> gap> rels:=[(F.1)^4, (F.2)^(10), (F.1)*(F.2)*(F.1)^(-1)*(F.2)^(-3)]; [ f1^4, f2^10, f1*f2*f1^-1*f2^-3 ] gap> G:=F/rels; <fp group on the generators [ f1, f2 ]> gap> Display(G); generators = [ f1, f2 ] relators = [ f1^4, f2^10, f1...

 
1 hour later…
KReiser
KReiser
22:54
@Shaun As pointed out in a comment on your answer by aschepler, "no, because my computer said so" doesn't really help the OP understand how to answer their question - indeed, the last line of their question is "So what can I do next to prove that it is impossible?" and you haven't really addressed that.
I note that a couple months ago basically the same thing happened, see the transcript here and here. When people want to understand why or how, computer code saying "yes" or "no" rarely is enough by itself to constitute a full answer, and this is probably why you're getting downvotes on these sorts of answers.
Shaun
Shaun
23:13
Thank you, @KReiser.

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