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Automorphisms of Finite Groups

  • Inder Bir Singh Passi
  • Mahender Singh
  • Manoj Kumar Yadav

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
    Pages 1-28
  3. Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
    Pages 29-67
  4. Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
    Pages 69-116
  5. Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
    Pages 117-155
  6. Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
    Pages 157-193
  7. Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
    Pages 195-208
  8. Back Matter
    Pages 209-217

About this book

Introduction

The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.

Keywords

Automorphism Central automorphism Coclass tree Divisibility Property Group cohomology Schur multiplier Uniform Lie algebra Wells exact sequence Group extension

Authors and affiliations

  • Inder Bir Singh Passi
    • 1
  • Mahender Singh
    • 2
  • Manoj Kumar Yadav
    • 3
  1. 1.Centre for Advanced Study in MathematicsPanjab UniversityChandigarhIndia
  2. 2.Department of Mathematical SciencesIndian Institute of Science Education and Research, MohaliSAS NagarIndia
  3. 3.School of MathematicsHarish-Chandra Research Institute HBNIJhunsi AllahabadIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-2895-4
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-13-2894-7
  • Online ISBN 978-981-13-2895-4
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site