- #1
PsychonautQQ
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Homework Statement
Let Q < L < Q(c) where c is a primitive nth root of unity over Q. Is [L:Q] a Galois extension?
Homework Equations
The Attempt at a Solution
L must be equal to Q(d) where d is a non primitive nth root of unity. [Q(d):Q] is not a galois extension because the minimal polynomial of d over Q is x^d -1, and this polynomial has d roots, not all of which are in Q. Is this correct?