On maximal subgroups of the multiplicative group of a division algebra

JOURNAL OF ALGEBRA

卷:322

Article

Hazrat, R.²  Wadsworth, A. R.¹ 

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Queens Univ Belfast, Dept Pure Math, Belfast BT7 1NN, Antrim, North Ireland

关键词: Division algebras;    Multiplicative group;    Maximal subgroup;   

DOI  :  10.1016/j.jalgebra.2009.01.009

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free