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

Details Realizability and admissibility under extension of p-adic and number fields Realizability and admissibility under extension of p-adic and number fields

2009-11-19

arxiv.org/abs/0911.3792v2

Mathematics

Rings and Algebras

22 pages

Scientific paper

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.

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