1. The problem statement, all variables and given/known data Let Q < L < Q(c) where c is a primitive nth root of unity over Q. Is [L:Q] a Galois extension? 2. Relevant equations 3. 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?