03899nam 22007455 450 99646637490331620200704121925.03-540-78584-110.1007/978-3-540-78584-2(CKB)1000000000437230(SSID)ssj0000316137(PQKBManifestationID)11232666(PQKBTitleCode)TC0000316137(PQKBWorkID)10263640(PQKB)10023668(DE-He213)978-3-540-78584-2(MiAaPQ)EBC3068748(PPN)12521846X(EXLCZ)99100000000043723020100301d2008 u| 0engurnn|008mamaatxtccrAlgebraic Groups and Lie Groups with Few Factors[electronic resource] /by Alfonso Di Bartolo, Giovanni Falcone, Peter Plaumann, Karl Strambach1st ed. 2008.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2008.1 online resource (XVI, 212 p.)Lecture Notes in Mathematics,0075-8434Bibliographic Level Mode of Issuance: Monograph3-540-78583-3 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.Lecture Notes in Mathematics,0075-8434Group theoryAlgebraic geometryTopological groupsLie groupsNonassociative ringsRings (Algebra)Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Non-associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11116Group 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.516.35Di Bartolo Alfonsoauthttp://id.loc.gov/vocabulary/relators/aut504067Falcone Giovanniauthttp://id.loc.gov/vocabulary/relators/autPlaumann Peterauthttp://id.loc.gov/vocabulary/relators/autStrambach Karlauthttp://id.loc.gov/vocabulary/relators/autBOOK996466374903316Algebraic Groups and Lie Groups with Few Factors2831405UNISA