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ON UNRAMIFIED SOLVABLE EXTENSIONS OF SMALL NUMBER FIELDS
Bulletin of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2020-11-09 , DOI: 10.1017/s0004972720001136
JOACHIM KÖNIG

We investigate unramified extensions of number fields with prescribed solvable Galois group G 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 for nilpotent groups.

中文翻译:

关于小数字领域的未分类可解决扩展

我们研究了具有规定的可解伽罗瓦群的数域的非分支扩展G和某些额外条件。特别是,我们对数域的最小度感兴趣ķ, 伽罗瓦结束$\mathbb {Q}$, 这样ķ拥有一个完整的G-延期。我们改进了此类数域度数的最佳已知界限ķ对于某些类别的可解群,尤其是幂零群。
更新日期:2020-11-09
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