English

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

R2 v1 2026-06-21T19:22:31.824Z