Tits Alternative for Maximal Subgroups of Skew Linear Groups

Abstract

Let D be a noncommutative finite dimensional F-central division algebra, and let N be a normal subgroup of GL _n (D) with n ≥ 1. Given a maximal subgroup M of N, it is proved that either M contains a noncyclic free subgroup, or there exists an abelian subgroup A and a finite family of fields properly containing F with for all 1 ≤ i ≤ r such that M/A is finite if Char F = 0 and M/A is locally finite if Char F = p > 0, where .

Key Words:

• Maximal subgroup
• Skew linear group

2000 Mathematics Subject Classification:

• 15A33
• 16K20

ACKNOWLEDGEMENTS

The authors thank the referee for constructive comments. The first author is indebted to the Institute for Studies in Theoretical Physics and Mathematics (IPM) for partial support (Grant No. 86150116). The second author thanks Professor Ulf Rehmann for his hospitality during his stay at the Bielefeld University in March 2006.

Notes

Communicated by H. Schneider.