On maximal Subgroups of the multiplicative group of a division algebra

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Hazrat, R.
Wadsworth, A. R.
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Abstract
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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.
Comment: 18 pages
Keywords
Mathematics - Rings and Algebras
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