r.hazrat@qub.ac.uk

Submission: 2007, May 14

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 $\ind(D)$ is not a power of $2$, $F^{*2}$ is divisible, and for each odd prime $p$ dividing $\ind(D)$, there exist noncyclic division algebras of degree $p$ over $F$.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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