Notes on Infinite Permutation Groups

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.

Sommario

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.

Dettagli sul prodotto

• Autori: Meenax Bhattacharjee, Meenaxi Bhattacharjee, Macphe, Dugald MacPherson, Rögnvaldur Möller, Rögnvaldur G Möller, Rögnvaldur G. Möller, Peter M. Neumann
• Editore: Springer, Berlin
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 01.01.2007
• EAN: 9783540649656
• ISBN: 978-3-540-64965-6
• Pagine: 202
• Peso: 324 g
• Serie: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Aritmetica, algebra