论文标题
在少量字段的未经验证的可解决的扩展方面
On unramified solvable extensions of small number fields
论文作者
论文摘要
我们研究了具有规定的可解决的GALOIS组和某些额外条件的数字字段的不受影响的扩展。特别是，我们对超过$ \ mathbb {q} $的数字字段$ k $的最小程度感兴趣，因此$ k $拥有一个未造成的$ g $ extension。对于某些类别的可解决方案组，尤其是Nilpotent群体，我们提高了此类数字字段$ K $的程度的最著名界限。
We investigate unramified extensions of number fields with prescribed solvable Galois group and certain extra conditions. In particular, we are interested in the minimal degree of a number field $K$, Galois over $\mathbb{Q}$, such that $K$ possesses an unramified $G$-extension. We improve the best known bounds for the degree of such number fields $K$ for certain classes of solvable groups, in particular nilpotent groups.
