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arXiv · 1110.4162

Fields of definition for admissible groups

Danny Neftin·Uzi Vishne
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Abstract

A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where the division algebra, the maximal subfield or the Galois group are asserted to be defined over K. We completely determine the logical implications between all variants.

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Danny Neftin, Uzi Vishne. 2011-10-19. Fields of definition for admissible groups. https://arxiv.org/abs/1110.4162

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