Algebraic Groups and Lie Groups with Few Factors [electronic resource] /
Di Bartolo, Alfonso.author.
Falcone, Giovanni.author.
Plaumann, Peter.author.
Strambach, Karl.author.
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.
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references and index.
Prerequisites -- Extensions -- Groups of Extreme Nilpotency Class -- Chains -- Groups with Few Types of Isogenous Factors -- Three-Dimensional Affine Groups -- Normality of Subgroups.
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.
Group theory.
Algebraic geometry.
Topological groups.
Lie groups.
Nonassociative rings.
Rings (Algebra).
Group Theory and Generalizations.
Algebraic Geometry.
Topological Groups, Lie Groups.
Non-associative Rings and Algebras.
Lecture notes in mathematics