English

On maximal Subgroups of the multiplicative group of a division algebra

Rings and Algebras 2008-12-19 v1

Abstract

The question of existence of a maximal subgroup in the multiplicative group D* of a division algebra D finite dimensional over its center F is investigated. We prove that if D* has no maximal subgroup, then deg(D) is not a power of 2, F^{*2} is divisible, and for each odd prime p dividing deg(D), there exist noncyclic division algebras of degree p over F.

Keywords

Cite

@article{arxiv.0812.3435,
  title  = {On maximal Subgroups of the multiplicative group of a division algebra},
  author = {R. Hazrat and A. R. Wadsworth},
  journal= {arXiv preprint arXiv:0812.3435},
  year   = {2008}
}

Comments

18 pages