D. Kiani, M. Mahdavi-Hezavehi: Tits Alternative for Maximal Subgroups of Skew Linear Groups

dkiani@aut.ac.ir, mahdavih@sharif.edu

Submission: 2006, Mar 22

Let $ D $ be a noncommutative finite dimensional $ F $-central division algebra, and let $ N $ be a normal subgroup of $ GL_n(D) $ with $ n \geq 1 $. Given a maximal subgroup $ M $ of $ N $, it is proved that either $M$ contains a noncyclic free subgroup or there exist an abelian subgroup $ A $ and a finite family $\{K_i\}^r_1$ of fields properly containing $ F $ with $ K^*_i \subset M $ for all $1\leq i\leq r$ such that $M/A$ is finite if $ Char F = 0 $ and $ M/A $ is locally finite if $ Char F = p>0 $, where $A \subseteq K^*_1 \times \cdots \times K^*_r$.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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