Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups

Name: Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups
Price: 101.37 AUD
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ISBN: 9783030959555

Nick Gill, Martin W. Liebeck, Pablo Spiga

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English

Springer Nature Switzerland AG
18 June 2022

Mathematical foundations; Mathematical logic; Groups & group theory

Series: Lecture Notes in Mathematics

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.

By: Nick Gill, Martin W. Liebeck, Pablo Spiga
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2302
Dimensions: Height: 235mm, Width: 155mm,
Weight: 355g
ISBN: 9783030959555
ISBN 10: 3030959554
Series: Lecture Notes in Mathematics
Pages: 216
Publication Date: 18 June 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Introduction.- 2. Preliminary Results for Groups of Lie Type.- 3. Exceptional Groups.- 4. Classical Groups.

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.

Reviews for Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups

“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)