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$\begingroup$

Show that the even subgroup of ${\bf F}_2$ is generated by $S= \{x^{2}, xy, xy^{-1}\}$. I could use a little help getting started on this problem. I am new to the idea of free groups.

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    Sorry... what is the even subgroup of a free group?2011-11-19
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    From what I can understand, an even subfroup of a free group contains as its elements, words of even length.2011-11-20

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