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.
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Mathematics
, 2025, Issue 1, pp. 1–10
ISSN Online: 0000-0000
DOI:
10.xxxx/example-doi