kiani@mehr.sharif.edu, mahdavih@sharif.edu
Submission: 2004, Jan 19
Let $D$ be a finite dimensional $ F $-central division algebra. A criterion is given for $ D $ to be a supersoluble (nilpotent) crossed product division algebra in terms of subgroups of the multiplicative group $D^*$ of $D$. More precisely, it is shown that $D$ is supersoluble (nilpotent) crossed product if and only if $D^*$ contains an irreducible abelian-by-supersoluble (nilpotent) subgroup.
2000 Mathematics Subject Classification:
Keywords and Phrases:
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