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Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups

  • Book
  • © 2022

Overview

Authors:
  1. Nick Gill

    1. School of Mathematics and Statistics, The Open University, Milton Keynes, UK

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  2. Martin W. Liebeck

    1. Department of Mathematics, Imperial College London, London, UK

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  3. Pablo Spiga

    1. Dipartimento di Matematica pura e Applicata, University of Milano-Bicocca, Milano, Italy

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  • Provides a solution to the Cherlin conjecture on binary groups
  • Gives a classification of the finite binary relational structures
  • Includes a comprehensive review of previous work on finite primitive binary permutation groups

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2302)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Nick Gill, Martin W. Liebeck, Pablo Spiga
    Pages 1-36

  3. Preliminary Results for Groups of Lie Type

    • Nick Gill, Martin W. Liebeck, Pablo Spiga
    Pages 37-69

  4. Exceptional Groups

    • Nick Gill, Martin W. Liebeck, Pablo Spiga
    Pages 71-101

  5. Classical Groups

    • Nick Gill, Martin W. Liebeck, Pablo Spiga
    Pages 103-207

  6. Back Matter

    Pages 209-216
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Keywords

About this book

This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. 


The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. 


Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest toa wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.



Reviews

“This monograph proves an attractive conjecture of G. L. Cherlin on finite permutation groups, motivated by model theory.” (H. Dugald Macpherson, Mathematical Reviews, November, 2023)

Authors and Affiliations

  • School of Mathematics and Statistics, The Open University, Milton Keynes, UK

    Nick Gill

  • Department of Mathematics, Imperial College London, London, UK

    Martin W. Liebeck

  • Dipartimento di Matematica pura e Applicata, University of Milano-Bicocca, Milano, Italy

    Pablo Spiga

About the authors

​Nick Gill is a Lecturer in Pure Mathematics at the Open University. 

Martin Liebeck has been Professor of Pure Mathematics at Imperial College London for over 30 years. He haspublished over 150 research articles and 10 books. His research interests include group theory, combinatorics and computational algebra. He was elected Fellow of the America Mathematical Society in 2019, and was awarded the London Mathematical Society's Polya Prize in 2020. 


Pablo Spiga is Professor of Mathematics at the University of Milano-Bicocca. His main research interests involve group actions on graphs and other combinatorial structures. His main expertise is within finite primitive groups and their application for investigating symmetries of combinatorial structures.

Bibliographic Information

  • Book Title: Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups

  • Authors: Nick Gill, Martin W. Liebeck, Pablo Spiga

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-95956-2

  • Publisher: Springer Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Softcover ISBN: 978-3-030-95955-5Published: 18 June 2022

  • eBook ISBN: 978-3-030-95956-2Published: 17 June 2022

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 216

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Group Theory and Generalizations, Mathematical Logic and Foundations

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