论文标题
关于一些假想二次领域的班级组的指数
On the exponents of class groups of some families of imaginary quadratic fields
论文作者
论文摘要
令$ a \ geq 1 $，$ n> 1 $为奇数。对于给定的Prime $ p $，我们在某些条件下证明了一个假想二次字段的组组$ \ mathbb {q}（\ sqrt {\ sqrt {a^2-4p^n}）$具有子组为$ \ $ \ \ \ \ \ m m mathbb {z}/n \ mathbb {Z} $。我们还表明，这个领域的家族具有无限的属性成员，其班级组具有一个子组同构为$ \ Mathbb {z}/n \ mathbb {z} $。此外，我们推断出一些关于某些假想二次场的班级数量的无条件结果。最后，我们提供了一些数值示例来验证我们的结果。
Let $a\geq 1$ and $n>1$ be odd integers. For a given prime $p$, we prove under certain conditions that the class groups of imaginary quadratic fields $\mathbb{Q}(\sqrt{a^2-4p^n})$ have a subgroup isomorphic to $\mathbb{Z}/n\mathbb{Z}$. We also show that this family of fields has infinitely many members with the property that their class groups have a subgroup isomorphic to $\mathbb{Z}/n\mathbb{Z}$. In addition, we deduce some unconditional results concerning the divisibility of the class numbers of certain imaginary quadratic fields. At the end, we provide some numerical examples to verify our results.
