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arXiv · 0812.3435

On maximal Subgroups of the multiplicative group of a division algebra

R. Hazrat·A. R. Wadsworth
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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.

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R. Hazrat, A. R. Wadsworth. 2008-12-17. On maximal Subgroups of the multiplicative group of a division algebra. https://arxiv.org/abs/0812.3435

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