On maximal subgroups of the multiplicative group of a division algebra |
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| Authors: | R Hazrat AR Wadsworth |
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| Institution: | aDepartment of Pure Mathematics, Queen's University, Belfast BT7 1NN, United Kingdom;bDepartment of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, USA |
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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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| Keywords: | Division algebras Multiplicative group Maximal subgroup |
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