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?