R. Ebrahimian, D. Kiani, M. Mahdavi-Hezavehi: Supersoluble Crossed Product Criterion for Division Algebras

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:

Full text: dvi.gz 13 k, dvi 32 k, ps.gz 516 k, pdf.gz 91 k, pdf 112 k.

Server Home Page