Deependra Singh
Emory University
Title
Admissibility of Sylow-metacyclic groups over number fields
Abstract
Given a field K, one can ask which finite groups G are Galois groups of field extensions L/K such that L is a maximal subfield of a division algebra with center K. Such a group G is called admissible over K. Like the inverse Galois problem, the question remains open in general. But unlike the inverse Galois problem, the groups that occur in this fashion are generally quite restricted. For example, a result of Sonn says that a solvable group is admissible over the rational numbers if and only if the group is Sylow-metacyclic. In this talk, I will discuss an extension of this result, classifying the number fields for which every solvable Sylow-metacyclic group is tamely admissible.