Groups

An Introduction to Ideas and Methods of the Theory of Groups

  • Antonio Machì

Part of the UNITEXT book series (UNITEXT)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Antonio Machì
    Pages 1-37
  3. Antonio Machì
    Pages 87-153
  4. Antonio Machì
    Pages 155-204
  5. Antonio Machì
    Pages 205-252
  6. Antonio Machì
    Pages 253-288
  7. Antonio Machì
    Pages 289-325
  8. Antonio Machì
    Pages 327-362
  9. Back Matter
    Pages 363-378

About this book

Introduction

Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.

Keywords

Cohomology Group actions Relations Representations

Authors and affiliations

  • Antonio Machì
    • 1
  1. 1.Department of MathematicsUniversity La SapienzaRomeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-470-2421-2
  • Copyright Information Springer-Verlag Milan 2012
  • Publisher Name Springer, Milano
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-88-470-2420-5
  • Online ISBN 978-88-470-2421-2
  • Series Print ISSN 2038-5714
  • About this book