Embedding problems with local conditions and the admissibility of finite groups

Details Embedding problems with local conditions and the admissibility of finite groups Embedding problems with local conditions and the admissibility of finite groups

2011-02-19

arxiv.org/abs/1102.3984v1

Mathematics

Number Theory

8 pages

Scientific paper

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.

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