Show that is not isomorphic to , where is the group of units in . i.e.
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Suppose that is isomorphic to Let \mathbf{R},+)\to (\mathbf{R}^*.\cdot)" alt="f\mathbf{R},+)\to (\mathbf{R}^*.\cdot)" /> an isomorphism. Then For Then f is not a surjection.
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