Skip to main content
  • Book
  • © 2009

Classical Finite Transformation Semigroups

An Introduction

  • First book about transformation semigroups
  • First book presenting results from former Soviet Union semigroup schools
  • Easy to read, although fully detailed with many examples
  • Can be used both as an introduction to transformation semigroups and abstract semigroups
  • Has many historical remarks and open questions for further research

Part of the book series: Algebra and Applications (AA, volume 9)

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
  2. Ordinary and Partial Transformations

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 1-14
  3. The Semigroups T n, PT n, and IS n

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 15-38
  4. Generating Systems

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 39-43
  5. Ideals and Green ' s Relations

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 45-67
  6. Subgroups and Subsemigroups

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 69-89
  7. Other Relations on Semigroups

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 91-110
  8. Endomorphisms

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 111-129
  9. Nilpotent Subsemigroups

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 131-152
  10. Presentation

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 153-174
  11. Transitive Actions

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 175-188
  12. Linear Representations

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 189-213
  13. Cross-Sections

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 215-236
  14. Variants

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 237-250
  15. Order-Related Subsemigroups

    • Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 251-275
  16. Back Matter

    Pages 277-314

About this book

The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but also to tutors and researchers.

Reviews

From the reviews:

"The book is self-contained and so accessible to university students. … the book will be an excellent source of ideas for graduate students in transformation semigroups as it lays out a pattern of research topics for the reader to consider. … The book is rich in exercises; the topic lends to it, and there are hints and answers where appropriate. There is also a good bibliography and notation list … overall the text is up-to-date and does a thorough job." (P. M. Higgins, Mathematical Reviews, Issue 2009 i)

“The reader is introduced to the basics of abstract semigroup theory. … at the end of each chapter a section with additional problems appears, some of which are easy exercises while others are more advanced (solutions of them are given in an appendix). The book is primarily directed to students who make their first steps in semigroup theory … .” (H. Mitsch, Monatshefte für Mathematik, Vol. 159 (4), March, 2010)

Authors and Affiliations

  • Kyiv Taras Shevchenko University, Kyiv, Ukraine

    Olexandr Ganyushkin

  • Dept. Mathematics, Uppsala University, Uppsala, Sweden

    Volodymyr Mazorchuk

Bibliographic Information

  • Book Title: Classical Finite Transformation Semigroups

  • Book Subtitle: An Introduction

  • Authors: Olexandr Ganyushkin, Volodymyr Mazorchuk

  • Series Title: Algebra and Applications

  • DOI: https://doi.org/10.1007/978-1-84800-281-4

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London 2009

  • Hardcover ISBN: 978-1-84800-280-7Published: 23 December 2008

  • Softcover ISBN: 978-1-84996-768-6Published: 28 October 2010

  • eBook ISBN: 978-1-84800-281-4Published: 10 December 2008

  • Series ISSN: 1572-5553

  • Series E-ISSN: 2192-2950

  • Edition Number: 1

  • Number of Pages: XII, 328

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Group Theory and Generalizations, Combinatorics

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access