Let n be an integer. Then, it is well known that there are infinitely many imaginary quadratic fields with an ideal class group having a subgroup isomorphic to ZZ x ZZ. Less is known for real quadratic fields, other than the cases that n = 3, 5, or 7, due to Craig [3] and Mestre [4, 5]. In this article, we will prove that there exist infinitely many real quadratic number fields with the ideal class group having a subgroup isomorphic to ZZ x ZZ In addition, we will prove that there exist infinitely many imaginary quadratic number fields with the ideal class group having a subgroup isomorphic to ZZ x ZZ x ZZ.
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机译：令n为整数。然后，众所周知的是，存在具有理想类别组的无限多个虚二次域，理想类别组具有与Z / nZ x Z / nZ同构的子组。由于克雷格[3]和麦斯特[4，5]，除了n = 3、5或7的情况外，对于实数二次域知之甚少。在本文中，我们将证明存在无限多个实二次数字段，理想类组的子组与Z / nZ x Z / nZ同构。此外，我们将证明存在无限多个虚二次数字段，其中具有与Z / nZ x Z / nZ x Z / nZ同构的子组的理想类组。
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