  A finite group G is called admissible over a given field if there exists a
central division algebra that contains a G-Galois field extension as a maximal
subfield. We give a definition of embedding problems of division algebras that
extends both the notion of embedding problems of fields as in classical Galois
theory, and the question which finite groups are admissible over a field. In a
recent work by Harbater, Hartmann and Krashen, all admissible groups over
function fields of curves over complete discretely valued fields with
algebraically closed residue field of characteristic zero have been
characterized. We show that also certain embedding problems of division
algebras over such a field can be solved for admissible groups.
