Galois extension, lattice of subfields

  • Thread starter mathsss2
  • Start date
  • #1
38
0
[tex]K=\mathbb{Q}(\sqrt{2+\sqrt{2}})[/tex] is a Galois extension of [tex]\mathbb{Q}[/tex] [I showed this]. Determine [tex]\text{Gal}(K/\mathbb{Q})[/tex] and describe the lattice of subfields [tex]\mathbb{Q} \subset F \subset K[/tex].

I found that [tex]\text{Gal}(K/\mathbb{Q})=\mathbb{Z}_4[/tex]. I do not know how to draw the lattice of subfields, so far I have this: [see attachment], but I do not think it is right. I need help with the lattice of subfields.
 

Attachments

  • 1.PNG
    1.PNG
    2.6 KB · Views: 355

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
4,627
634
Recall that the lattice of subfields is directly correlated to the lattice of subgroups of the galois group. This should make it easier
 

Related Threads on Galois extension, lattice of subfields

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
3K
Replies
5
Views
4K
Replies
5
Views
917
Replies
7
Views
3K
Replies
6
Views
1K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
2K
Top