I'm asked to find the Galois group of this polynomial over Q:
x^5-2x^3-x^2+2.
This is irreducible over Q, but over Fp where p is prime, the polynomial factorises. Does this information help, or is there a different way to find the Galois group?
I'm asked to find the Galois group of this polynomial over Q:
x^5-2x^3-x^2+2.
This is irreducible over Q, but over Fp where p is prime, the polynomial factorises. Does this information help, or is there a different way to find the Galois group?