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I have a question about the solvable group.

I read a Fraleigh's 'A first course in abstract algebra', there is a question in sec56, exercise3.

It says "The Galois group of a finite extension of a finite field is solvable." is true....

I can't figure out why it's true.

I think this means "every finite polynomial of finite field F is solvable by radicals." (it's correct?)

Help...