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Embedding problems with local conditions and the admissibility of finite groups

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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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Authors and Affiliations

  1. FB6, Mathematik, Universität Duisburg-Essen, 45117, Essen, Germany

    NguyỄn Duy Tân

  2. Institute of Mathematics, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam

    NguyỄn Duy Tân

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  1. NguyỄn Duy Tân
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Correspondence to NguyỄn Duy Tân.

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Partially supported by NAFOSTED, the SFB/TR45 and the ERC/Advanced Grant 226257.

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Tân, N.D. Embedding problems with local conditions and the admissibility of finite groups. Isr. J. Math. 198, 229–242 (2013). https://doi.org/10.1007/s11856-013-0018-7

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  • DOI: https://doi.org/10.1007/s11856-013-0018-7

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