Tamely ramified subfields of division algebras

JOURNAL OF ALGEBRA

卷:378

Article

Neftin, Danny

关键词: Admissibility;    Division algebras;    Crossed products;    Embedding problems;    Inverse Galois problem;   

DOI  :  10.1016/j.jalgebra.2012.11.039

来源: Elsevier

【 摘 要 】

For any number field K, it is unknown which finite groups appear as Galois groups of extensions L/K such that L is a maximal subfield of a division algebra with center K (a K-division algebra). For K = Q, the answer is described by the long standing Q-admissibility conjecture. We extend a theorem of Neukirch on embedding problems with local constraints in order to determine for every number field K, what finite solvable groups G appear as Galois groups of tamely ramified maximal subfields of K-division algebras, generalizing Liedahl's theorem for metacyclic G and Sonn's solution of the Q-admissibility conjecture for solvable groups. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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