
Cherlin's Conjecture for Finite Primitive Binary Permutation Groups
Springer (Publisher)
1st Edition
Published on 18. June 2022
Book
Paperback/Softback
IX, 216 pages
978-3-030-95955-5 (ISBN)
Description
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 to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
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 to a 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 / Votes
"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)More details
Product info
Paperback
Series
Edition
1st ed. 2022
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
1
1 s/w Abbildung
IX, 216 p. 1 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 13 mm
Weight
353 gr
ISBN-13
978-3-030-95955-5 (9783030959555)
DOI
10.1007/978-3-030-95956-2
Schweitzer Classification
Other editions
Additional editions

Nick Gill | Martin W. Liebeck | Pablo Spiga
Cherlin's Conjecture for Finite Primitive Binary Permutation Groups
E-Book
06/2022
Springer
€58.84
Available for download
Persons
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.
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.
Content
1. Introduction.- 2. Preliminary Results for Groups of Lie Type.- 3. Exceptional Groups.- 4. Classical Groups.