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April 29th, 2009, 12:25 AM   #1
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Extension Fields/Galios

f degree n poly over Q
K the splitting field of f
Gal(K/Q) isomorphic to

a. proved f irreducible since if it were, [K:Q]<n!

so here is where the question begins for me

b. if n>2 and a root of f(x) in K, show

i claimed that since [K:Q]=n!, then K must be a separable extension since f deg n so [K:Q] is the largest it can be ... then roots go to roots and there is only on root in Q(a) so we're done. is this right?

c. if show that

not really sure how to start this one

any nudges in the right direction are greatly appreciated.
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