Show that the union of , where is from to , is a (profinite) normal extension of
And show that its Galois group is the additive group of the integer 2-adic number.
Last edited by ZetaX; April 20th 2009 at 09:18 AM.
Show that the union of , where is from to , is a (profinite) normal extension of
And show that its Galois group is the additive group of the integer 2-adic number.
well, is normal because is abelian and thus each is normal. i'm not expert in infinite Galois theory but i'm pretty sure the key to the second part of your
problem is this isomorphism: now the question is what exactly is ?