On maximal subgroups of the multiplicative group of a division algebra

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• 作者：R. Hazrat ; A.R. Wadsworth
• 关键词：Division algebras ; Multiplicative group ; Maximal subgroup
• 刊名：Journal of Algebra
• 出版年：2009
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：1 October 2009
• 卷：322
• 期：7
• 页码：2528-2543
• 文件大小：274 K

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.