Cherlin's Conjecture for Finite Primitive Binary Permutation Groups
Cherlin's Conjecture for Finite Primitive Binary Permutation Groups
复制标题
切尔林有限原二元置换群猜想
DOI：
10.1007/978-3-030-95956-2
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Gill N
中科院分区：
文献类型：
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作者：
Gill N
本文给出了有限二元原始置换群的Cherlin猜想的证明。受拉克兰有限齐次关系结构理论部分模型理论的启发，该猜想提出了关系复杂度等于2的有限原始排列群的分类。第一部分对Cherlin猜想进行了全面的介绍，包括所有在文献中用来证明其某些特殊情况的关键思想。第二部分通过处理几乎简单的原始置换群来完成证明。本文包含了大量关于原始置换群和几乎单群性质的材料，并引入了一些新的思想。解决了一个热门话题，它跨越了群论，模型理论和逻辑的学科，这本书将感兴趣的广泛的读者。它对需要处理简单李型群的研究生和研究人员特别有用。
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.