division algebras的弱分歧子域
Tamely ramified subfields of division algebras
摘要：
对于任意数域K，未知哪些有限群表现为扩张L/K的伽罗瓦群，使得L是以K为中心的除代数（K-除代数）的极大子域。对于K=Q，答案由长期存在的Q-容许性猜想描述。本文推广了Neukirch关于带局部约束的嵌入问题的一个定理，以确定对于任意数域K，什么样的有限可解群G表现为K-除代数的驯服极大子域的伽罗瓦群，推广了亚循环G的Liedahl定理和可解群的Q-容许猜想的Sonn解.
英文摘要：
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 tame 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.
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