TY - BOOK ID - 93582810 TI - Algebraic Groups and Lie Groups with Few Factors AU - Bartolo, Alfonso AU - Falcone, Giovanni AU - Plaumann, Peter AU - Strambach, Karl AU - SpringerLink (Online service) PY - 2008 SN - 9783540785842 PB - Berlin, Heidelberg Springer-Verlag Berlin Heidelberg DB - UniCat KW - Group theory KW - Ordered algebraic structures KW - Topological groups. Lie groups KW - Geometry KW - algebra KW - landmeetkunde KW - topologie (wiskunde) KW - wiskunde UR - https://www.unicat.be/uniCat?func=search&query=sysid:93582810 AB - 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. ER -