Radical and Cyclotomic Extensions of the Rational Numbers
نویسنده
چکیده
A radical extension of the rational numbers Q is a field R ⊇ Q generated by an element having a power in Q, and a cyclotomic extension K ⊇ Q is an extension generated by a root of unity. We show that a radical extension that is almost Galois over Q is almost cyclotomic. More precisely, we prove that if R is radical with Galois closure E, then E contains a cyclotomic field K such that the degree |E : K| is bounded above by an almost linear function of |E : R|. In particular, if R is Galois, it contains a cyclotomic field K such that |R : K| ≤ 3.
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