Cherlins Conjecture for Finite Primitive Binary Permutation Groups (Paperback)

Nick Gill

ISBN 10: 3030959554 / ISBN 13: 9783030959555

Published by Springer Nature Switzerland AG, Cham, 2022

About this Item

Paperback. This book gives a proof of Cherlins conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlans 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 Cherlins 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. This book gives a proof of Cherlins conjecture for finite binary primitive permutation groups. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Seller Inventory # 9783030959555

Bibliographic Details

• Title: Cherlins Conjecture for Finite Primitive Binary Permutation Groups (Paperback)
• Publisher: Springer Nature Switzerland AG, Cham
• Publication Date: 2022
• Language: English
• ISBN 10: 3030959554
• ISBN 13: 9783030959555
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

About the Author

​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 has

published 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.