Doubly transitive Galois group and specializations
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
I read here in Lemma 1 that if $alpha$ is a root of $x^n+ax+b $ and $fracx^n-alpha^nx-alpha=a$ is irreducible over $k(a,b,alpha) = k(a,alpha)$ then the Galois group $G$ is doubly transitive.
I guess that, here the Galois group of specialized polynomial, i.e., by making the variable $b=0$ is doubly transitive. Then how the Galois group of original polynomial is doubly transitive?
please help. Any hint is of immense help.
galois-theory irreducible-polynomials
add a comment |Â
up vote
0
down vote
favorite
I read here in Lemma 1 that if $alpha$ is a root of $x^n+ax+b $ and $fracx^n-alpha^nx-alpha=a$ is irreducible over $k(a,b,alpha) = k(a,alpha)$ then the Galois group $G$ is doubly transitive.
I guess that, here the Galois group of specialized polynomial, i.e., by making the variable $b=0$ is doubly transitive. Then how the Galois group of original polynomial is doubly transitive?
please help. Any hint is of immense help.
galois-theory irreducible-polynomials
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I read here in Lemma 1 that if $alpha$ is a root of $x^n+ax+b $ and $fracx^n-alpha^nx-alpha=a$ is irreducible over $k(a,b,alpha) = k(a,alpha)$ then the Galois group $G$ is doubly transitive.
I guess that, here the Galois group of specialized polynomial, i.e., by making the variable $b=0$ is doubly transitive. Then how the Galois group of original polynomial is doubly transitive?
please help. Any hint is of immense help.
galois-theory irreducible-polynomials
I read here in Lemma 1 that if $alpha$ is a root of $x^n+ax+b $ and $fracx^n-alpha^nx-alpha=a$ is irreducible over $k(a,b,alpha) = k(a,alpha)$ then the Galois group $G$ is doubly transitive.
I guess that, here the Galois group of specialized polynomial, i.e., by making the variable $b=0$ is doubly transitive. Then how the Galois group of original polynomial is doubly transitive?
please help. Any hint is of immense help.
galois-theory irreducible-polynomials
galois-theory irreducible-polynomials
edited Sep 6 at 7:52
asked Sep 6 at 5:35
user86925
639517
639517
add a comment |Â
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2907126%2fdoubly-transitive-galois-group-and-specializations%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password