Notes on Infinite Permutation Groups / Edition 1

by Meenaxi Bhattacharjee, Rïgnvaldur G. Mïller, Dugald Macpherson, Peter M. Neumann

Overview

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.

Product Details

ISBN-13:	9783540649656
Publisher:	Springer Berlin Heidelberg
Publication date:	12/10/1998
Series:	Lecture Notes in Mathematics , #1698
Edition description:	1998
Pages:	206
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Some group theory.- Groups acting on sets.- Transitivity.- Primitivity.- Suborbits and orbitals.- More about symmetric groups.- Linear groups.- Wreath products.- Rational numbers.- Jordan groups.- Examples of Jordan groups.- Relations related to betweenness.- Classification theorems.- Homogeneous structures.- The Hrushovski construction.- Applications and open questions.