I was thinking about the following proposition that I think should be true, but I can't pove:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that F is a group freely generated by a set U and that F is also generated by a set V with |U| = |V|. Then F is also freely generated by V.

This is something that I intuitively think must be true when considering examples I have come across e.g( F_2 = <a,b> = <a,ab> with {a,b} and {a,ab} both free generating sets). Does anyone know if this is true?

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# Understanding generating sets for free groups.

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