I'm trying to show that a group generated by elements $x,y,z$ with a given relation $xyxz^{-2}=1$ (where $1$ is the identity) is in fact a free group.
What are some usual ways of going about this kind of problem? Just hints please!
Regards
2026-03-29 12:05:29.1774785929
Proving that a group generated by x,y and z and a given relation is actually free
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Are you aware of the relations of your problem to the subject of presentation of groups, in general, and in particular to the Nielsen-Schreier therorem and Nielsen transformations? This should qualify as one of the "usual ways" of going about this kind of problem at least.