I have some questions on the field extension $\overline{\mathbb{F}_p}|\mathbb{F}p$ for some prime number $p$: Are the any other intermediate fields besides $\mathbb{F}{p^n}$ for $n \in \mathbb{N}$ or $\overline{\mathbb{F}_p}$? What is the Galois group of the extension $\overline{\mathbb{F}_p}|\mathbb{F}_p$? Do we have that $\overline{\mathbb{F}p}= \cup{n=1}^{\infty} \mathbb{F}_{p^n}$?
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closed as off topic by Andreas Blass, Felipe Voloch, Cam McLeman, Joe Silverman, JSE Aug 13 2011 at 21:48 |
