2009/10/21 by Danny Neftin, Neftin, Danny
Mathematics · #11R32 #11R52 #12F12 #16S35 #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11R32 #msc:11R52 #msc:12F12 #msc:16S35
paper · pdf · doi:10.48550/arxiv.0910.4156
18 pages
arxiv created 2011/11/22 · arxiv updated 2011/11/23
Let K be a number field. A finite group G is called K-admissible if there exists a G-crossed product K-division algebra. K-admissibility has a necessary condition called K-preadmissibility that is known to be sufficient in many cases. It is a 20 year old open problem to determine whether two number fields K and L with different degrees over Q can have the same admissible groups. We construct infinitely many pairs of number fields (K,L) such that K is a proper subfield of L and K and L have the same preadmissible groups. This provides evidence for a negative answer to the problem. In particular, it follows from the construction that K and L have the same odd order admissible groups.