# Math Help - Galois group of the algebraic closure of the rationals

1. ## Galois group of the algebraic closure of the rationals

An absolutely fascinating object since we know so little about it. I'd love to learn more but I haven't been able to find much information.

I do not know anything about it myself but I would imagine you need to know infinite Galois theory. That is when $K/F$ is a Galois extension but $[K:F] = \infty$. The standard results to the study of subgroups $\text{Gal}(K/F)$ no longer apply, only very specific subgroups are now considered. Have you ever seen this kind of stuff before?
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