Model Theory of Groups and Automorphism Groups

by Edited by David M. Evans

• ISBN13: 9780521589550
• ISBN10: 052158955X
• Format: Paperback
• Copyright: 1997-08-13
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction	ix
D. M. Evans
D. Macpherson
A. A. Ivanov
Finite covers	1	(72)
Z. Chatzidakis
Definable subgroups of algebraic groups over pseudo-finite fields	73	(17)
W. Hodges
Groups in pseudofinite fields	90	(20)
D. Lascar
The group of automorphisms of the field of complex numbers leaving fixed the algebraic numbers is simple	110	(5)
D. Evans
D. Lascar
The automorphism group of the field of complex numbers is complete	115	(11)
P. J. Cameron
The algebra of an age	126	(8)
M. Boffa
Elimination of inverses in groups	134	(10)
F. Oger
Model-theoretic properties of polycyclic-by-finite groups	144	(9)
I. M. Chiswell
Non-standard free groups	153	(13)
P. H. Pfander
Finitely generated subgroups of the free Z[t]-group on two generators	166	(22)
K. Burke
M. Prest
Rings of definable scalars and biendomorphism rings	188	(14)
B. Kim
Recent results on simple first-order theories	202