2009/04/24 by Danny Neftin, Neftin, Danny
Mathematics · #16S35 #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:16S35
paper · pdf · doi:10.48550/arxiv.0904.3772
arxiv created 2012/10/01 · arxiv updated 2012/10/02
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.