Isomorphisms of Galois groups

  title={Isomorphisms of Galois groups},
  author={K{\^o}ji Uchida},
  journal={Journal of The Mathematical Society of Japan},
  • Kôji Uchida
  • Published 1 October 1976
  • Mathematics
  • Journal of The Mathematical Society of Japan
Let $Q$ be the field of the rational numbers. Let $\Omega$ be a normal algebraic extension of $Q$ such that $\Omega$ has no abelian extension. Let $G$ be the Galois group of $\Omega$ over $Q$ . Neukirch $[4, 5]$ has shown that every open normal subgroup of $G$ is a characteristic subgroup, and has proposed a problem whether every automorphism of $G$ is inner. In this paper this problem is solved affirmatively, $i$ . $e.$ , we prove THEOREM. Let $G_{1}$ and $G_{2}$ be open subgroups of $G$ , and… 
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