Embedding problems with local conditions and the admissibility of finite groups |
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Authors: | Nguy?n Duy Tân |
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Institution: | 1. FB6, Mathematik, Universit?t Duisburg-Essen, 45117, Essen, Germany 2. Institute of Mathematics, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam
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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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