Galois group of a extension of $mathbbC (X,Y)$ [on hold] The Next CEO of Stack OverflowHow to describe when a simple extension $F(alpha)/F$ is Galois in terms of the minimal polynomial of $alpha$?degree 3 Galois extension of $mathbbQ$ not radicalprove that the Galois group $Gal(L:K)$ is cyclicHow to show that any field extension $K/mathbbQ$ of degree 4 that is not Galois has a quadratic extension $L$ that is Galois over $mathbbQ$.Galois extension and Galois groupFind all Galois extensions of degree 6 of $K=mathbbC(S,T,U)$Why is this not a Galois extensionFind Galois group of $mathbbQ ( sqrtp)/mathbbQ$Finding Galois group of finite field extensionGalois extension in $mathbbC$
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Galois group of a extension of $mathbbC (X,Y)$ [on hold]
The Next CEO of Stack OverflowHow to describe when a simple extension $F(alpha)/F$ is Galois in terms of the minimal polynomial of $alpha$?degree 3 Galois extension of $mathbbQ$ not radicalprove that the Galois group $Gal(L:K)$ is cyclicHow to show that any field extension $K/mathbbQ$ of degree 4 that is not Galois has a quadratic extension $L$ that is Galois over $mathbbQ$.Galois extension and Galois groupFind all Galois extensions of degree 6 of $K=mathbbC(S,T,U)$Why is this not a Galois extensionFind Galois group of $mathbbQ ( sqrtp)/mathbbQ$Finding Galois group of finite field extensionGalois extension in $mathbbC$
$begingroup$
Let $mathbbC(X,Y)$ be rational function field over $mathbbC$ .
We consider a extension $L=mathbbC(X,Y) / mathbbC(X^n+Y^n,X^nY^n)=K$ for some $n in mathbbN$.
Then, I have two questions.
$(1)$ How large is the extension degree $[L:K]$ $??$
$(2)$ $L/K$ is fnite Galois extension $??$
complex-numbers field-theory galois-theory rational-functions galois-extensions
asked 2 days ago
神宮寺春姫神宮寺春姫
412
$endgroup$
put on hold as off-topic by Saad, Wojowu, Riccardo.Alestra, egreg, jgon yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Wojowu, Riccardo.Alestra, egreg, jgon
add a comment |
$begingroup$
Let $mathbbC(X,Y)$ be rational function field over $mathbbC$ .
We consider a extension $L=mathbbC(X,Y) / mathbbC(X^n+Y^n,X^nY^n)=K$ for some $n in mathbbN$.
Then, I have two questions.
$(1)$ How large is the extension degree $[L:K]$ $??$
$(2)$ $L/K$ is fnite Galois extension $??$
complex-numbers field-theory galois-theory rational-functions galois-extensions
asked 2 days ago
神宮寺春姫神宮寺春姫
412
$endgroup$
put on hold as off-topic by Saad, Wojowu, Riccardo.Alestra, egreg, jgon yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Wojowu, Riccardo.Alestra, egreg, jgon
$begingroup$
This question doesn't make sense because $K$ is not a subfield of $L$.
$endgroup$
– Wojowu
2 days ago
$begingroup$
@Wojowu , sorry. I correct setting of $L/K$.
$endgroup$
– 神宮寺春姫
yesterday
1
$begingroup$
$[mathbbC(X,Y):mathbbC(X,Y^n)] = n$ (minimal polynomial $t^n-Y^n$ for $t=Y$) and $[mathbbC(X,X^n Y^n):mathbbC(X^n+Y^n,X^nY^n)] = 2n$. Do you have a guess for the latter minimal polynomial and for the automorphism groups ?
$endgroup$
– reuns
yesterday
add a comment |
$begingroup$
Let $mathbbC(X,Y)$ be rational function field over $mathbbC$ .
We consider a extension $L=mathbbC(X,Y) / mathbbC(X^n+Y^n,X^nY^n)=K$ for some $n in mathbbN$.
Then, I have two questions.
$(1)$ How large is the extension degree $[L:K]$ $??$
$(2)$ $L/K$ is fnite Galois extension $??$
complex-numbers field-theory galois-theory rational-functions galois-extensions
asked 2 days ago
神宮寺春姫神宮寺春姫
412
$endgroup$
Let $mathbbC(X,Y)$ be rational function field over $mathbbC$ .
We consider a extension $L=mathbbC(X,Y) / mathbbC(X^n+Y^n,X^nY^n)=K$ for some $n in mathbbN$.
Then, I have two questions.
$(1)$ How large is the extension degree $[L:K]$ $??$
$(2)$ $L/K$ is fnite Galois extension $??$
complex-numbers field-theory galois-theory rational-functions galois-extensions
complex-numbers field-theory galois-theory rational-functions galois-extensions
asked 2 days ago
神宮寺春姫神宮寺春姫
412
asked 2 days ago
神宮寺春姫神宮寺春姫
412
edited yesterday
神宮寺春姫
asked 2 days ago
神宮寺春姫神宮寺春姫
412
asked 2 days ago
神宮寺春姫神宮寺春姫
412
asked 2 days ago
神宮寺春姫神宮寺春姫
412
412
put on hold as off-topic by Saad, Wojowu, Riccardo.Alestra, egreg, jgon yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Wojowu, Riccardo.Alestra, egreg, jgon
put on hold as off-topic by Saad, Wojowu, Riccardo.Alestra, egreg, jgon yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Wojowu, Riccardo.Alestra, egreg, jgon
$begingroup$
This question doesn't make sense because $K$ is not a subfield of $L$.
$endgroup$
– Wojowu
2 days ago
$begingroup$
@Wojowu , sorry. I correct setting of $L/K$.
$endgroup$
– 神宮寺春姫
yesterday
1
$begingroup$
$[mathbbC(X,Y):mathbbC(X,Y^n)] = n$ (minimal polynomial $t^n-Y^n$ for $t=Y$) and $[mathbbC(X,X^n Y^n):mathbbC(X^n+Y^n,X^nY^n)] = 2n$. Do you have a guess for the latter minimal polynomial and for the automorphism groups ?
$endgroup$
– reuns
yesterday
add a comment |
$begingroup$
This question doesn't make sense because $K$ is not a subfield of $L$.
$endgroup$
– Wojowu
2 days ago
$begingroup$
@Wojowu , sorry. I correct setting of $L/K$.
$endgroup$
– 神宮寺春姫
yesterday
1
$begingroup$
$[mathbbC(X,Y):mathbbC(X,Y^n)] = n$ (minimal polynomial $t^n-Y^n$ for $t=Y$) and $[mathbbC(X,X^n Y^n):mathbbC(X^n+Y^n,X^nY^n)] = 2n$. Do you have a guess for the latter minimal polynomial and for the automorphism groups ?
$endgroup$
– reuns
yesterday
$begingroup$
This question doesn't make sense because $K$ is not a subfield of $L$.
$endgroup$
– Wojowu
2 days ago
$begingroup$
This question doesn't make sense because $K$ is not a subfield of $L$.
$endgroup$
– Wojowu
2 days ago
$begingroup$
@Wojowu , sorry. I correct setting of $L/K$.
$endgroup$
– 神宮寺春姫
yesterday
$begingroup$
@Wojowu , sorry. I correct setting of $L/K$.
$endgroup$
– 神宮寺春姫
yesterday
1
1
$begingroup$
$[mathbbC(X,Y):mathbbC(X,Y^n)] = n$ (minimal polynomial $t^n-Y^n$ for $t=Y$) and $[mathbbC(X,X^n Y^n):mathbbC(X^n+Y^n,X^nY^n)] = 2n$. Do you have a guess for the latter minimal polynomial and for the automorphism groups ?
$endgroup$
– reuns
yesterday
$begingroup$
$[mathbbC(X,Y):mathbbC(X,Y^n)] = n$ (minimal polynomial $t^n-Y^n$ for $t=Y$) and $[mathbbC(X,X^n Y^n):mathbbC(X^n+Y^n,X^nY^n)] = 2n$. Do you have a guess for the latter minimal polynomial and for the automorphism groups ?
$endgroup$
– reuns
yesterday
add a comment |
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$begingroup$
This question doesn't make sense because $K$ is not a subfield of $L$.
$endgroup$
– Wojowu
2 days ago
$begingroup$
@Wojowu , sorry. I correct setting of $L/K$.
$endgroup$
– 神宮寺春姫
yesterday
1
$begingroup$
$[mathbbC(X,Y):mathbbC(X,Y^n)] = n$ (minimal polynomial $t^n-Y^n$ for $t=Y$) and $[mathbbC(X,X^n Y^n):mathbbC(X^n+Y^n,X^nY^n)] = 2n$. Do you have a guess for the latter minimal polynomial and for the automorphism groups ?
$endgroup$
– reuns
yesterday