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:

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