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Lower Central and Dimension Series of Groups

  • Roman Mikhailov
  • Inder Bir Singh Passi

Part of the Lecture Notes in Mathematics book series (LNM, volume 1952)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Pages 1-100
  3. Pages 101-164
  4. Pages 165-185
  5. Pages 187-227
  6. Pages 229-290
  7. Pages 291-297
  8. Back Matter
    Pages 299-352

About this book

Introduction

A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.

Keywords

DEX Group rings Groups Simplical Objects addition group group theory object

Authors and affiliations

  • Roman Mikhailov
    • 1
  • Inder Bir Singh Passi
    • 2
  1. 1.Department of AlgebraSteklov Mathematical InstituteMoscowRussia
  2. 2.Centre for Advanced Study in MathematicsPanjab UniversityChandigarhIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-85818-8
  • Copyright Information Springer Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-85817-1
  • Online ISBN 978-3-540-85818-8
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site