R. Ebrahimian, D. Kiani, M. Mahdavi-Hezavehi: Irreducible Subgroups of $GL_1(D)$ Satisfying Group Identities

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:

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