Cherlin's conjecture on finite primitive binary permutation groups
File(s)
Supporting information
Author(s)
Liebeck, Martin
Gill, Nick
Spiga, Pablo
Type
Book
Abstract
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.
Date Issued
2022-06-18
Citation
2022, 2302
ISBN
978-3-030-95955-5
Publisher
Springer Verlag
Journal / Book Title
Lecture Notes in Mathematics
Volume
2302
Copyright Statement
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022. The final publication is available at Springer via https://link.springer.com/book/10.1007/978-3-030-95956-2
Subjects
01 Mathematical Sciences
General Mathematics
Publication Status
Published