ebrahimian@mehr.sharif.edu, kiani@mehr.sharif.edu, mahdavih@sharif.edu

Submission: 2003, Nov 20

Let $D$ be a finite dimensional $ F $-central division algebra, and $G$ be an irreducible subgroup of $D^*:=GL_1(D)$. Here we investigate the structure of $D$ under various group identities on $G$. In particular, it is shown that when $[D:F]=p^2$, $p$ a prime, then $D$ is cyclic if and only if $D^*$ contains a nonabelian subgroup satisfying a group identity.

2000 Mathematics Subject Classification:

Keywords and Phrases:

Full text: dvi.gz 15 k, dvi 37 k, ps.gz 554 k, pdf.gz 96 k, pdf 119 k.