Embedding problems with local conditions and the admissibility of finite groups

2011/02/19 by Nguyen Duy Tan, Tan, Nguyen Duy
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1102.3984

8 pages

arxiv created 2011/02/19 · arxiv updated 2011/02/22

Abstract

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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