Thread: 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.

If anyone can shed a tiny bit of light about this for me, please do so!

Originally Posted by Bruno J.

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.

If anyone can shed a tiny bit of light about this for me, please do so!

I do not know anything about it myself but I would imagine you need to know infinite Galois theory. That is when is a Galois extension but . The standard results to the study of subgroups no longer apply, only very specific subgroups are now considered. Have you ever seen this kind of stuff before?