Fields of definition for admissible groups
Rings and Algebras
2011-10-20 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.1110.4162,
title = {Fields of definition for admissible groups},
author = {Danny Neftin and Uzi Vishne},
journal= {arXiv preprint arXiv:1110.4162},
year = {2011}
}
Comments
11 pages. arXiv admin note: text overlap with arXiv:0911.3792