Notes on Infinite Permutation Groups

1998
ISBN: 978-3-540-64965-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1698, 206 Seiten, Paperback, Format (B × H): 155 mm x 233 mm, Gewicht: 338 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bhattacharjee, Meenaxi

Neumann, Peter M.

Möller, Rögnvaldur G.

Macpherson, Dugald

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.