Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $$\mathbb{Q}\left( {\sqrt {{x^2} - 2{y^n}} } \right)$$ 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.

中文翻译：

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某虚二次域类群的指数

令 n > 1 为奇数。我们证明有无穷多个形如 $$\mathbb{Q}\left( {\sqrt {{x^2} - 2{y^n}} } \right)$$ 的虚二次域，它们的理想类群有一个 n 阶元素。该族给出了 H. Wada (1970) 关于理想类群结构的猜想的反例。