Algebraic groups and Lie groups with fewfactors

Algebraic groups are treated here from a group the-oretical point of view and the obtained results are compared withthe analogous issues in the theory of Lie groups. The main bodyof the text is devoted to a classification of algebraic groups andLie groups having only few subgroups or few factor groups of dif-ferent type. In particular, the diversity of the nature of algebraicgroups over fields of positive characteristic and over fields of char-acteristic zero is emphasized. This is revealed by the plethora ofthree-dimensional unipotent algebraic groups over a perfect fieldof positive characteristic, as well as, by many concrete exampleswhich cover an area systematically. In the final section, algebraicgroups and Lie groups having many closed normal subgroups aredetermined.