This volume surveys recent interactions between model theory and other branches of mathematics, notably group theory. Beginning with an introductory chapter describing relevant background material, the book contains contributions from many leading international figures in this area. Topics described include automorphism groups of algebraically closed fields, the model theory of pseudo-finite fields and applications to the subgroup structure of finite Chevalley groups. Model theory of modules, and aspects of model theory of various classes of groups, including free groups, are also discussed. The book also contains the first comprehensive survey of finite covers. Many new proofs and simplifications of recent results are presented and the articles contain many open problems. This book will be a suitable guide for graduate students and a useful reference for researchers working in model theory and algebra.
The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts:...
This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks,...