ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: Akbari, S., Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran Multiplicative Subgroups of Division Rings Let D be a finite dimensional division ring over its center F. As a generalization of Wedderburn’s theorem it is proved that non-centeral normal subgroups of division rings can not be finitely generated. We conjecture that every division ring has at least one maximal subgroup. It seems that maximal subgroups of any non-commutative division ring can not be solvable. Also it is shown that if a maximal subgroup of D^{∗} = D−{0} is radical over F then D is commutative.