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 $H = Gal(L/(K \cap K^{'}))$.
-
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.
Answer
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
1 Attachment
- answered
- 165 views
- $20.00
Related Questions
-
The given equation is x² - 2mx + 2m - 1=0
Determine m. - Populace Model
- Does $\lim_{(x,y)\rightarrow (0,0)}\frac{(x^2-y^2) \cos (x+y)}{x^2+y^2}$ exists?
- Mechanical principle help (maths)
- Representation theory question
- Solve this problem using branch and bound algorithm.
- Guywire, finding height of the powerpole
- Determine the Closed Form of a Recurrance Relation