Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups

Beschreibung

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.

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.

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

Autor*in

Nick Gill

Themen in »Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups«

Combinatorics Finite Primitive Groups Binary Permutation Groups Relational Complexity Binary Relational Structures Almost Simple Groups Cherlin Conjecture Lachlan Theory on Homogeneous Structures

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“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)
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