Let $K$ be a Galois number field with cyclic Galois group. Let $L$ be an abelian Galois number field such that $K\subseteq L$. Suppose that there are no Galois subextensions $\mathbb Q\subseteq F \subseteq L$ such that $\text{Gal}(F/\mathbb Q)$ is cyclic and $K\subsetneq F$.

Is it true then that the exact sequence $1\to \text{Gal}(L/K)\to \text{Gal}(L/\mathbb Q)\to \text{Gal}(K/\mathbb Q)\to 1$ splits?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.