ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Mahdavi–Hezavehi, M., Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran Maximal subgroups of GL_{1}(D) Let D be an F -central division algebra of index m. Denote by D^{∗} = GL_{1}(D) the multiplicative group of D. Maximal subgroups of D^{∗} are investigated. It is shown that, except in some pathalogical cases, D^{∗} contains maximal subgroups of finite index. Given a maximal subgroup M of D^{∗}, it is shown that M contains an element not in F which is separable over F provided that the characteristic of D does not divide m. It is also proved that if M is torsion, then D = F. Reference: M. Mahdavi-Hezavehi, On derived groups of division rings, Communications in Algebra , Vol.23(3), 913-926(1995).