How to check if permutation induces an element of the Galois group.
$begingroup$
Let $f in mathbb Q[X]$ be irreducible of degree $n$ with zeros $alpha_1,dots,alpha_n in mathbb C$. Further, let $L$ be the splitting field of $f$ and $sigma in S_n$.
Is there an easy way to check if $ alpha_i mapsto alpha_{sigma(i)} $ induces an automorphism of $L$?
number-theory permutations galois-theory symmetric-groups
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
$endgroup$
add a comment |
$begingroup$
Let $f in mathbb Q[X]$ be irreducible of degree $n$ with zeros $alpha_1,dots,alpha_n in mathbb C$. Further, let $L$ be the splitting field of $f$ and $sigma in S_n$.
Is there an easy way to check if $ alpha_i mapsto alpha_{sigma(i)} $ induces an automorphism of $L$?
number-theory permutations galois-theory symmetric-groups
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
$endgroup$
$begingroup$
Voted to close as too broad... no, there isn't an easy way to check it.
$endgroup$
– Kenny Lau
Dec 31 '18 at 22:41
add a comment |
$begingroup$
Let $f in mathbb Q[X]$ be irreducible of degree $n$ with zeros $alpha_1,dots,alpha_n in mathbb C$. Further, let $L$ be the splitting field of $f$ and $sigma in S_n$.
Is there an easy way to check if $ alpha_i mapsto alpha_{sigma(i)} $ induces an automorphism of $L$?
number-theory permutations galois-theory symmetric-groups
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
$endgroup$
Let $f in mathbb Q[X]$ be irreducible of degree $n$ with zeros $alpha_1,dots,alpha_n in mathbb C$. Further, let $L$ be the splitting field of $f$ and $sigma in S_n$.
Is there an easy way to check if $ alpha_i mapsto alpha_{sigma(i)} $ induces an automorphism of $L$?
number-theory permutations galois-theory symmetric-groups
number-theory permutations galois-theory symmetric-groups
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
asked Dec 11 '18 at 15:57
principal-ideal-domainprincipal-ideal-domain
2,756522
2,756522
$begingroup$
Voted to close as too broad... no, there isn't an easy way to check it.
$endgroup$
– Kenny Lau
Dec 31 '18 at 22:41
add a comment |
$begingroup$
Voted to close as too broad... no, there isn't an easy way to check it.
$endgroup$
– Kenny Lau
Dec 31 '18 at 22:41
$begingroup$
Voted to close as too broad... no, there isn't an easy way to check it.
$endgroup$
– Kenny Lau
Dec 31 '18 at 22:41
$begingroup$
Voted to close as too broad... no, there isn't an easy way to check it.
$endgroup$
– Kenny Lau
Dec 31 '18 at 22:41
add a comment |
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$begingroup$
Voted to close as too broad... no, there isn't an easy way to check it.
$endgroup$
– Kenny Lau
Dec 31 '18 at 22:41