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
CONTENT
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
