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Divisibility of class numbers of certain cyclic fields. (Divisibilité du nombre de classes de certains corps cycliques.) (French) Zbl 0404.12004
Astérisque 61, 193-203 (1979).
Let $$\ell$$ be a prime number $$(\neq 2)$$, let $$n=\ell^r$$ be a power of $$\ell$$ and let $$\varphi$$ be the Euler function. We look at the cyclic extensions of $$\mathbb Q$$ of degree $$\varphi(n)$$ which contain the maximal real subfield of the $$n$$th cyclotomic field. We show the existence of infinitely many such fields (both real and imaginary) whose ideal class group contains an element of order $$n$$.
For the entire collection see [Zbl 0394.00007].
MSC:
 11R29 Class numbers, class groups, discriminants 11R11 Quadratic extensions 11R18 Cyclotomic extensions