Geodesic
Realizability and admissibility under extension of $p$-adic and number fields.
Documenta mathematica, Tome 18 (2013), pp. 359-382
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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.
DOI : 10.4171/dm/401
Classification : 12F12, 16K20
Mots-clés : admissible group, adequate field, tame admissibility, Liedahl's condition 
@article{10_4171_dm_401,
     author = {Danny Neftin and Uzi Vishne},
     title = {Realizability and admissibility under extension of $p$-adic and number fields.},
     journal = {Documenta mathematica},
     pages = {359--382},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/401},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/401/}
}
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Danny Neftin; Uzi Vishne. Realizability and admissibility under extension of $p$-adic and number fields.. Documenta mathematica, Tome 18 (2013), pp. 359-382. doi: 10.4171/dm/401

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