21
$\begingroup$

It is well-known that Galois correspondence sends a normal subgroup to a normal extension of a field. Specifically, given a Galois extension $L/K$ and the corresponding Galois group $G$, normal subgroups of $G$ correspond to normal subextensions $F/K$ .

Is there a characterization of the subextensions corresponding to characteristic subgroups?

$\endgroup$
0
1
+100
$\begingroup$

That question doesn't make sense because automorphisms of $Gal(L/K)$ don't have any meaning in Galois theory.

Only the inner automorphisms have a meaning, and a subgroup sent to itself by every inner automorphism is called a normal subgroup.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.