how can i calculate number of automorphism in a group
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heyya frnds.
_______
I've been given a field L=Q(4
√
2
) and I have to find Aut(
L
Q
).
Now i know that 4
√
2
has minimal polynomial x4−2 over Q, hence [L:Q]=4, so a Q basis for L has 4 elements, with two of them being 1 and 4
√
2
but I cannot figure out other two.
In terms of finding the automorphisms σ, I know that if we let σ∈Aut(
L
Q
) then σ is determined by σ(4
√
2
), and from here I am not quite sure how to calculate the group of automorphisms...
__^___^__
THANK YOU
@srk6
_______
I've been given a field L=Q(4
√
2
) and I have to find Aut(
L
Q
).
Now i know that 4
√
2
has minimal polynomial x4−2 over Q, hence [L:Q]=4, so a Q basis for L has 4 elements, with two of them being 1 and 4
√
2
but I cannot figure out other two.
In terms of finding the automorphisms σ, I know that if we let σ∈Aut(
L
Q
) then σ is determined by σ(4
√
2
), and from here I am not quite sure how to calculate the group of automorphisms...
__^___^__
THANK YOU
@srk6
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