Meenaxi Bhattacharjee, Dugald Macpherson, Rögnvaldur G. Möller, Peter M. Neumann (auth.)3540649654, 9783540649656
The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory. |
Table of contents :
Some group theory….Pages 1-8
Groups acting on sets….Pages 9-18
Transitivity….Pages 19-30
Primitivity….Pages 31-38
Suborbits and orbitals….Pages 39-48
More about symmetric groups….Pages 49-56
Linear groups….Pages 57-66
Wreath products….Pages 67-76
Rational numbers….Pages 77-86
Jordan groups….Pages 87-97
Examples of Jordan groups….Pages 99-113
Relations related to betweenness….Pages 115-129
Classification theorems….Pages 131-142
Homogeneous structures….Pages 143-158
The Hrushovski construction….Pages 159-170
Applications and open questions….Pages 171-180 |
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