Any Automorphism of the Field of Real Numbers Must be the Identity Map
Problem 507
Prove that any field automorphism of the field of real numbers $\R$ must be the identity automorphism.
Add to solve later Tagged: real numbers
Add to solve later Multiplicative Groups of Real Numbers and Complex Numbers are not Isomorphic
Problem 130
Let $\R^{\times}=\R\setminus \{0\}$ be the multiplicative group of real numbers.
Let $\C^{\times}=\C\setminus \{0\}$ be the multiplicative group of complex numbers.
Then show that $\R^{\times}$ and $\C^{\times}$ are not isomorphic as groups.
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