  A finite group G is K-admissible if there exists a G-crossed product
K-division algebra. In this manuscript we study the behavior of admissibility
under extensions of number fields M/K. We show that in many cases, including
Sylow metacyclic and nilpotent groups whose order is prime to the number of
roots of unity in M, a K-admissible group G is M-admissible if and only if G
satisfies the easily verifiable Liedahl condition over M.
