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Commutator subgroup does not consist only of commutators?
I am looking for an simple example (i.e. for undergraduate students) of group whose commutators $xyx^{1}y^{1}$ do not form a subgroup.
I am looking for an simple example (i.e. for undergraduate students) of group whose commutators $xyx^{1}y^{1}$ do not form a subgroup. 


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