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© 2008

Algebraic Groups and Lie Groups with Few Factors

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1944)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Pages 1-10
  3. Pages 11-28
  4. Pages 49-79
  5. Pages 167-198
  6. Back Matter
    Pages 199-206

About this book

Introduction

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.

Keywords

Dimension algebraic group commutative algebra lattice of subgroups maximal nilpotency class permutable subgroups semi-commutative algebraic and Lie groups unipotent groups

Authors and affiliations

  1. 1.Università degli Studi di Palermo90123Italy
  2. 2.Università degli Studi di Palermo90138Italy
  3. 3.Mathematisches Institut91054Germany

Bibliographic information

Reviews

From the reviews:

"This is a self-contained carefully written lecture note on algebraic groups as well as real and complex Lie groups. For algebraic groups the authors stress the difference between groups over fields of characteristic zero and characteristic p. … Overall the notes provide an excellent introduction to the subject and this research monograph presents remarkable and powerful results. It is a good reference for researchers working on groups outside the family of reductive groups." (Jorge A. Vargas, Mathematical Reviews, Issue 2009 g)

“The authors study both algebraic groups and real and complex Lie groups by imposing on their connected subgroups the analogues of familiar conditions in abstract group theory. … This book serves as a valuable resource to those working in the field of algebraic groups and as a good place to learn about this aspect of that field.” (Ernest L. Stitzinger, Zentralblatt MATH, Vol. 1176, 2010)