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

Danny Neftin; Uzi Vishne

doi:https://doi.org/10.4171/dm/401

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

Danny Neftin, Uzi Vishne

Technion - Israel Institute of Technology, Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

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 fieldsM/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.

Original language	English
Pages (from-to)	359-382
Number of pages	24
Journal	Documenta Mathematica
Volume	18
Issue number	2013
DOIs	https://doi.org/10.4171/dm/401
State	Published - 2013

Keywords

Adequate field
Admissible group
Liedahl's condition
Tame ad-missibility

All Science Journal Classification (ASJC) codes

General Mathematics

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Cite this

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abstract = "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 fieldsM/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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KW - Admissible group

KW - Liedahl's condition

KW - Tame ad-missibility

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M3 - مقالة

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JO - Documenta Mathematica

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ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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