Realizability and Admissibility under Extension of p-Adic and Number Fields

A finite group $G$ is $K$-admissible if there is 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 $M$.

2010 Mathematics Subject Classification: 16K20, 12F12

Keywords and Phrases: admissible group; adequate field; tame admissibility; Liedahl's condition.

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