Recent content by minibear

I have trouble in determining Galois group. Can anyone help me with the following question: how to determine the Galois group of (x^2-2)(x^2-3)(x^2-5), determine all the subfields of the splitting field of this polynomial? how to determine the elements of the galois group of x^p-2 for p...

Homework Statement Let (K, d) and (K', d') be two compact metric spaces and let f:K-->K' and g:K'--->K be isometries. Show that f(K)=K' and g(K')=K Homework Equations n/a The Attempt at a Solution I know that isometry implies that I can find one-to-one correspondence mapping, but...

The thing is: if you have (K, d) to be a compact metric space, then how to show (C(K) , d_infinity) is complete ?( d_infinity is uniform metric) I know maybe I should use Cauchy or triangle inequality, but I am just not clear how to construct the proof. Anyone who has any idea about that...

Thank you so much!

if K/E is a quadratic extension and field F is contained in K such that FE=K and [K:F] is finite, how do I give a non-example to show [F: F intersects E] might not be 2? Thanks a lot!