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.
Author(s): Meenaxi Bhattacharjee, Dugald Macpherson, Rögnvaldur G. Möller, Peter M. Neumann (auth.)
Series: Lecture Notes in Mathematics 1698
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1998
Language: English
Pages: 206
City: Berlin; New York
Tags: Group Theory and Generalizations
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