well you won't actually find three letters in an alphabet that only has two.
try this instead: prove that the subgroup generated by x^{2},xy and y^{2} is isomorphic to F_{3}.
Let be the free group on two generators . Prove that the free group on 3 generators is a subgroup of .
Not completely sure how to go about doing this. So . Can I show that z can be written as the the product of 's and 's and their inverses?
Or is there some other method I should try?
find three letters in an alphabet that only has two.
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