论文标题
二次数字字段，带有未受到的$ sl_2（5）$ - 扩展
Quadratic number fields with unramified $SL_2(5)$-extensions
论文作者
论文摘要
继续对较早的工作进行思路，我们提供了第一个无限的二次数字字段家族，到处都是Galois Group $ sl_2（5）$的无名Galois扩展，这是（独特的）最小的不可见名的组，以前为此问题开放。我们的方法还通过产生了拥有一个未受到的GALOIS扩展名的无限次数领域的无限家族，其方法也改善了以前的工作。我们的结果也等于在具有无方面判别和其他局部条件的五重数字字段上产生了新的存在。
Continuing the line of thought of an earlier work, we provide the first infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group $SL_2(5)$, the (unique) smallest nonsolvable group for which this problem was previously open. Our approach also improves upon previous work by yielding the first infinite family of real-quadratic fields possessing an unramified Galois extension whose Galois group is perfect and not generated by involutions. Our result also amounts to a new existence result on quintic number fields with squarefree discriminant and additional local conditions.
