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Divisibility of class numbers of imaginary quadratic fields whose discriminant has only two prime factors. (English) Zbl 1226.11117

Summary: Let \(g\geq 2\) and \(n\geq 1\) be integers. In this paper, we show that there are infinitely many imaginary quadratic fields whose class number is divisible by \(2g\) and whose discriminant has only two prime divisors. As a corollary, we show that there are infinitely many imaginary quadratic fields whose 2-class group is a cyclic group of order divisible by \(2^n\).

MSC:

11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
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References:

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