  Let D be a central division algebra of degree n over a field K. One defines
the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) of K
represented by central division algebras D' of degree n over K having the same
maximal subfields as D. We prove that if the field K is finitely generated and
n is prime to its characteristic, then gen(D) is finite, and give explicit
estimations of its size in certain situations.
