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It is known that every subgroup of an abelian group is normal . Does there exist a non-abelian group such that every subgroup of the group is normal ?

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marked as duplicate by Jack Schmidt group-theory May 25 '14 at 17:33

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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yes. these groups are called hamiltonian, see here: http://en.wikipedia.org/wiki/Hamiltonian_group the most popular example would be quaternions

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