Mathematics – Rings and Algebras
Scientific paper
2008-12-17
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.
Hazrat Roozbeh
Wadsworth Adrian R.
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