Hey there,(adsbygoogle = window.adsbygoogle || []).push({});

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:

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Galois Groups

**Physics Forums | Science Articles, Homework Help, Discussion**