Given an arbitrary group $ G $, in general does there exist a ring $ R $ with $ R^{\times} \cong G $? Or are there counterexamples of this?
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2Good question - See here for an answer - http://math.stackexchange.com/questions/384422/which-finite-groups-are-the-group-of-units-of-some-ring – Nicky Hekster Feb 23 '15 at 14:09