Skip to content
Register Sign in Wishlist
Look Inside Permutation Groups and Cartesian Decompositions

Permutation Groups and Cartesian Decompositions

£55.00

Part of London Mathematical Society Lecture Note Series

  • Date Published: May 2018
  • availability: In stock
  • format: Paperback
  • isbn: 9780521675062

£ 55.00
Paperback

Add to cart Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.

    • Contains a concise introduction to permutation group theory, quickly taking readers to an O'Nan–Scott theory for both primitive and quasiprimitive groups
    • Gives a rigorous treatment of cartesian decompositions that are invariant under permutation groups
    • Provides researchers with an easily accessible reference to results on group factorisations
    Read more

    Reviews & endorsements

    'This is a thorough reference book that consists of three parts … In summary, the book is an impressive collection of theorems and their proofs.' Miklós Bóna, MAA Reviews

    'One of the most important achievements of this book is building the first formal theory on G-invariant cartesian decompositions; this brings to the fore a better knowledge of the O'Nan–Scott theorem for primitive, quasiprimitive, and innately transitive groups, together with the embeddings among these groups. This is a valuable, useful, and beautiful book.' Pablo Spiga, Mathematical Reviews

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: May 2018
    • format: Paperback
    • isbn: 9780521675062
    • length: 334 pages
    • dimensions: 227 x 151 x 20 mm
    • weight: 0.5kg
    • contains: 2 b/w illus. 14 tables
    • availability: In stock
  • Table of Contents

    1. Introduction
    Part I. Permutation Groups – Fundamentals:
    2. Group actions and permutation groups
    3. Minimal normal subgroups of transitive permutation groups
    4. Finite direct products of groups
    5. Wreath products
    6. Twisted wreath products
    7. O'Nan–Scott theory and the maximal subgroups of finite alternating and symmetric groups
    Part II. Innately Transitive Groups – Factorisations and Cartesian Decompositions:
    8. Cartesian factorisations
    9. Transitive cartesian decompositions for innately transitive groups
    10. Intransitive cartesian decompositions
    Part III. Cartesian Decompositions – Applications:
    11. Applications in permutation group theory
    12. Applications to graph theory
    Appendix. Factorisations of simple and characteristically simple groups
    Glossary
    References
    Index.

  • Resources for

    Permutation Groups and Cartesian Decompositions

    Cheryl E. Praeger, Csaba Schneider

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact lecturers@cambridge.org.

  • Authors

    Cheryl E. Praeger, University of Western Australia, Perth
    Cheryl E. Praeger is Emeritus Professor at the Centre for the Mathematics of Symmetry and Computation at the University of Western Australia, Perth. She is an Honorary Life Member of the Australian Mathematical Society, and was its first female President. She has authored more than 400 research publications, including five books. Besides holding honorary doctorates awarded by universities in Thailand, Iran, Belgium, Scotland, and Australia, she is also a member of the Order of Australia for her service to mathematics in Australia.

    Csaba Schneider, Universidade Federal de Minas Gerais, Brazil
    Csaba Schneider is Professor in the Maths Department at the Federal University of Minas Gerais, Brazil. He has held research positions at the University of Western Australia, Perth, the Technical University of Braunschweig, the Hungarian Academy of Sciences, and the University of Lisbon. His mathematical interests include finite group theory, the theory of non-associative algebras, and computational algebra.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×