Neftin, Danny; Vishne, Uzi

Realizability and admissibility under extension of $p$-adic and number fields.

Doc. Math., J. DMV 18, 359-382 (2013)

Summary

Summary: 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 $M$.

Mathematics Subject Classification

16K20, 12F12

Keywords/Phrases

admissible group, adequate field, tame admissibility, Liedahl's condition

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