La Matematica per il 3+2

Groups

An Introduction to Ideas and Methods of the Theory of Groups

Authors: Machì, Antonio

  • More than 400 exercises for almost all of which a solution is provided, help the reader check his/her comprehension of the text
  • Some topics like representation theory, word problem or the meaning of some group-theoretic concepts in cohomology of groups are usually found in more specialized books
  • The meaning of some group-theoretic concepts in Galois theory
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eBook $44.99
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  • ISBN 978-88-470-2421-2
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  • Immediate eBook download after purchase
Softcover $59.95
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  • ISBN 978-88-470-2420-5
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About this Textbook

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.

Reviews

From the reviews:

“The book under review is appropriate for a student with at least one prior course in group theory. … Each chapter contains copious exercises, and answers to many of these exercises are provided at the end of the book. It is clear that the author wants the reader to see many interesting and important examples as soon as possible. This is one of the greatest strengths of the book nearly every section has several well-chosen illustrations of the theory.” (Adam Glesser, Mathematical Reviews, December, 2013)

“Aimed at … ‘advanced undergraduate and graduate students in mathematics, physics and chemistry’, it concentrates in 325 pages most of the important general techniques used in this field. … The book is written in a concise, but elegant style and manages to give the readers an introduction to many topics missing in similar texts … . In summary: this is a very good text, that matches well the declared aims … . It is also well suited as a reach and … compact reference text.” (Marian Deaconescu, Zentralblatt MATH, Vol. 1246, 2012)


Table of contents (8 chapters)

  • Introductory Notions

    Machì, Antonio

    Pages 1-37

  • Normal Subgroups, Conjugation and Isomorphism Theorems

    Machì, Antonio

    Pages 39-86

  • Group Actions and Permutation Groups

    Machì, Antonio

    Pages 87-153

  • Generators and Relations

    Machì, Antonio

    Pages 155-204

  • Nilpotent Groups and Solvable Groups

    Machì, Antonio

    Pages 205-252

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-88-470-2421-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-88-470-2420-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Groups
Book Subtitle
An Introduction to Ideas and Methods of the Theory of Groups
Authors
Series Title
La Matematica per il 3+2
Copyright
2012
Publisher
Springer-Verlag Mailand
Copyright Holder
Springer-Verlag Milan
eBook ISBN
978-88-470-2421-2
DOI
10.1007/978-88-470-2421-2
Softcover ISBN
978-88-470-2420-5
Series ISSN
2038-5722
Edition Number
1
Number of Pages
XIII, 371
Topics