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## Main Question or Discussion Point

Hey there,

firstly I hope that this is the right place to discuss such things. if not, could you direct me somewhere else?

Ok, I have to construct the Galois Group of f= (x^2-2x-1)^3 (x^2+x+1)^2 (x+1)^4 and then represent it as a permutation group of the roots.

first I constructed the splitting field extension S:Q (where S= summation symbol and Q = field of Rational numbers)

The splitting field i Came up with was Q(sqrt (2), sqrt (-3)):Q, and the degree of this splitting field is 4...am I correct here? is this the splitting field?

The Galois group represented as a permutation group I ended up getting was

{ e (the identity), (sqrt(-3),-sqrt(-3)),(sqrt(2),-sqrt(2)),(sqrt(2),-sqrt(2))(sqrt(-3),-sqrt(-3))}

isomorphic to the Klein4 group....

am i doing this right?? it just seems abit simple a result for an initial function that wasn't that simple ! :uhh:

firstly I hope that this is the right place to discuss such things. if not, could you direct me somewhere else?

Ok, I have to construct the Galois Group of f= (x^2-2x-1)^3 (x^2+x+1)^2 (x+1)^4 and then represent it as a permutation group of the roots.

first I constructed the splitting field extension S:Q (where S= summation symbol and Q = field of Rational numbers)

The splitting field i Came up with was Q(sqrt (2), sqrt (-3)):Q, and the degree of this splitting field is 4...am I correct here? is this the splitting field?

The Galois group represented as a permutation group I ended up getting was

{ e (the identity), (sqrt(-3),-sqrt(-3)),(sqrt(2),-sqrt(2)),(sqrt(2),-sqrt(2))(sqrt(-3),-sqrt(-3))}

isomorphic to the Klein4 group....

am i doing this right?? it just seems abit simple a result for an initial function that wasn't that simple ! :uhh: