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
3.5K
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
- 736 views
- $20.00
Related Questions
- Sinusodial graph help (electrical)
- Trying to solve this system of simultaneous equations. A solution with work shown would be appreciated.
- What is f(x). I've been trying to understand it for so long, but I always get different answers, I feel like I'm going crazy. Please someone explain it and read my whole question carefully.
- Algebra Word Problem #1
- Solving Inequalities- Erik and Nita are playing a game with numbers
- College Algebra 1
- Module isomorphism and length of tensor product.
- Find $x$ so that $\begin{pmatrix} 1 & 0 & c \\ 0 & a & -b \\ -\frac{1}{a} & x & x^2 \end{pmatrix}$ is invertible
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.