Algebraic groups and lie groups with few factors

Alfonso Di Bartolo, Giovanni Falcone, Peter Plaumann, Karl Strambach (auth.)9783540785835, 3540785833, 3540785841, 9783540785842

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

Table of contents :
Front Matter….Pages i-xvi
Prerequisites….Pages 1-10
Extensions….Pages 11-28
Groups of Extreme Nilpotency Class….Pages 29-47
Chains….Pages 49-79
Groups with Few Types of Isogenous Factors….Pages 81-147
Three-Dimensional Affine Groups….Pages 149-166
Normality of Subgroups….Pages 167-198
Back Matter….Pages 199-206