Armenian Journal of Mathematics

Algebraic groups and Lie groups with few factors

Strambach, Karl (2008) Algebraic groups and Lie groups with few factors. Armenian Journal of Mathematics, 1 (2). pp. 4-9. ISSN 1829-1163

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Algebraic groups are treated here 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.

Item Type:Article
Subjects:20-xx Group theory and generalizations
14-xx Algebraic geometry
ID Code:31
Deposited By:Professor Anry Nersesyan
Deposited On:13 Oct 2008 12:00
Last Modified:19 Apr 2011 02:22

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