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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].
11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
11R18 Cyclotomic extensions