局部条件嵌入问题与有限群的容许性
Embedding problems with local conditions and the admissibility of finite groups
摘要：
设$k$是一个具有特征$p>0$的域，它有无穷多个离散赋值。我们证明了每个有限嵌入问题的$\Gal(k)$与许多规定的局部条件，其核心是一个$p$ -群，是适当可解的。然后，我们应用这一结果研究了正特征整体域上有限群的可容许性。我们还对Sonn的一个结果给出了另一个证明。
英文摘要：
Let $k$ be a field of characteristic $p>0$, which has infinitely many discrete valuations. We show that every finite embedding problem for $\Gal(k)$ with finitely many prescribed local conditions, whose kernel is a $p$-group, is properly solvable. We then apply this result in studying the admissibility of finite groups over global fields of positive characteristic. We also give another proof for a result of Sonn.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
