When is Galois extension over intersection of subfields finite
Suppose that $K$ and $K^{'}$ are subfields of $L$ such that $ L/K$ (resp. $L/K^{'}$) is a Galois extension with Galois group $G$ (resp. $G^{'}$). Show that $L/(K \cap K^{'})$ is a Galois extension if and only if the group $H$, generated by $G$ and$ G^{'}$, is finite. Show furthermore that if this is so, then $H = Gal(L/(K \cap K^{'}))$.
Jbuck
152
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
Mathe
3.4K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 679 views
- $20.00
Related Questions
- Recursive square root sequence
- A Problem on Affine Algebraic Groups and Hopf Algebra Structures
- How do you go about solving this question?
- Stuck on this and need the answer for this problem at 6. Thanks
- Find $x$, if $\sqrt{x} + 2y^2 = 15$ and $\sqrt{4x} − 4y^2 = 6$.
- Prove that: |x| + |y| ≤ |x + y| + |x − y|.
- Compounding interest of principal P, where a compounding withdrawal amount W get withdrawn from P before each compounding of P.
- Simple equation?
I would suggest increasing the bounty.
Yes, the bounty is too low for the level of the question.
@Philip Hey there, I hope you're alright! I was wondering if you could help me with some questions this Friday, 10a.m. GMT +1. I will have around a 2-2.5 hour window and I'm willing to pay $60 per question if you're online and able to answer within the time limit, would you be interested? The questions are related to representation theory.