On maximal Subgroups of the multiplicative group of a division algebra

Details On maximal Subgroups of the multiplicative group of a division algebra On maximal Subgroups of the multiplicative group of a division algebra

2008-12-17

arxiv.org/abs/0812.3435v1

Mathematics

Rings and Algebras

18 pages

Scientific paper

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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