Armenian Journal of MathematicsVolume 1, Number 2
2008; 4–9
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Algebraic groups and Lie groups with fewfactors

Karl Strambach*

Received: 2024-11-29 · Published: 2008-11-13

© 2008 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Originally published in Armenian Journal of MathematicsVolume 1, Number 2, 2008.

Original title
Algebraic groups and Lie groups with fewfactors
Author
Karl Strambach
Source journal
Armenian Journal of MathematicsVolume 1, Number 2
Published
2008-11-13
Licence
Creative Commons Attribution 4.0 International
Original
https://armjmath.sci.am/index.php/ajm/article/view/22

Abstract

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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