Geodesic
Realizability and admissibility under extension of $p$-adic and number fields.
Documenta mathematica, Tome 18 (2013), pp. 359-382.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $M$.
Classification : 16K20, 12F12
Keywords: admissible group, adequate field, tame admissibility, Liedahl's condition 
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     author = {Neftin, Danny and Vishne, Uzi},
     title = {Realizability and admissibility under extension of $p$-adic and number fields.},
     journal = {Documenta mathematica},
     pages = {359--382},
     publisher = {mathdoc},
     volume = {18},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a37/}
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Neftin, Danny; Vishne, Uzi. Realizability and admissibility under extension of $p$-adic and number fields.. Documenta mathematica, Tome 18 (2013), pp. 359-382. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a37/