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Exponent of class group of certain imaginary quadratic fields

Kalyan Chakraborty, Azizul Hoque (2020)

Czechoslovak Mathematical Journal

Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form x 2 - 2 y n whose ideal class group has an element of order n . This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.

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