Embedding problems with local conditions and the admissibility of finite groups
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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.
KeywordsWeak Solution Exact Sequence Galois Group Division Algebra Sylow Subgroup
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