TY  - BOOK
AU  - Bartolo,Alfonso Di
AU  - Falcone,Giovanni
AU  - Plaumann,Peter
AU  - Strambach,Karl
ED  - SpringerLink (Online service)
TI  - Algebraic Groups and Lie Groups with Few Factors
T2  - Lecture Notes in Mathematics,
SN  - 9783540785842
AV  - QA174-183 
U1  - 512.2 23
PY  - 2008///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Algebraic geometry
KW  - Group theory
KW  - Nonassociative rings
KW  - Rings (Algebra)
KW  - Topological groups
KW  - Lie groups
KW  - Group Theory and Generalizations
KW  - Algebraic Geometry
KW  - Topological Groups, Lie Groups
KW  - Non-associative Rings and Algebras
N1  - Prerequisites -- Extensions -- Groups of Extreme Nilpotency Class -- Chains -- Groups with Few Types of Isogenous Factors -- Three-Dimensional Affine Groups -- Normality of Subgroups
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-540-78584-2
ER  -