Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $F/K$ be a finite extension of fields. $S$ the set of subgroups of $\mathrm{Aut}_K(F)$ and $I$ the set of intermediate fields of the extension $F/K$. Define the function $\varphi:S\rightarrow I$ as $\varphi(G)= F^G$ where $F_G$ is the subfield of $F$ fixed by $G$. Could you help me to find an example of extension $F/K$ where $\varphi$ is not surjective?

share|improve this question

1 Answer 1

up vote 3 down vote accepted

$K=\mathbb{Q}$, $F=K(\sqrt[4]{2})$, $G$ is the group oforder two.

There are 2 subgroups and 3 intermediate fields ($K$, $F$, and $K(\sqrt{2})$).

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.