Groups and model theory : a conference in honor of Rudiger Gobel's 70th birthday, May 30-June 3, 2011, Conference Center "Die Wolfsburg," Mulheim an der Ruhr, Germany / Lutz Strungmann [and three others], editors.

Format:

Book

Contributor:

Göbel, R. (Rüdiger), 1940- honouree.

Strungmann, Lutz, 1971- editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 576

Contemporary mathematics, 576 0271-4132

Language:

English

Subjects (All):

Group theory--Congresses.

Group theory.

Model theory--Congresses.

Model theory.

Physical Description:

1 online resource (336 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

This book contains the proceedings of the conference "Groups and Model Theory'', held May 30-June 3, 2011, in Ruhr, Germany, in honour of Rudiger Gobel's 70th birthday. In the last thirty years, group theory has received new input through the application of methods from logic to problems in algebra. In particular, model theory has strongly influenced both commutative and non-commutative group theory. This led to striking new developments in group theory and has had an interesting impact back on model theory. This interplay has been revisited by algebraists and model theorists and is showing strong and promising roads for future research. This book presents important current research at the border of model theory and group theory by renowned researchers. Articles in this volume cover abelian groups, modules over commutative rings, permutation groups, automorphism groups of homogeneous structures such as graphs, relational structures, geometries, topological spaces or groups, consequences of model theoretic properties like stability or categoricity, subgroups of small index, the automorphism tower problem, as well as random constructions.

Contents:

About the conference

A few words about Rudiger

Chapter 1.

Functorial properties of Hom and Ext

1. Introduction

2. Functors Acting on Sums and Products

3. Hom and Ext

4. -small groups

5. -extendible groups

References

Rigid abelian groups and the probabilistic method

2. The probabilistic method: A brief introduction

3. Groups via -adic numbers

4. Small-rank groups

5. Concluding remarks and open questions

6. Acknowledgments

On projection-invariant subgroups of Abelian -groups

2. Direct Powers

Looking for indecomposable right bounded complexes

Introduction

1. Preliminaries

2. Examples

Butler's theorem revisited

1. Notation and basic settings

2. Regularity

3. Previous results

4. The (1) case

5. The (2) case

6. The general case

7. The concrete solution

8. Cancelling Primes

9. Realizing the converse of Butler's Theorem

The role of the Jacobson radical in isomorphism theorems

2. Preliminaries

3. Determining the Torsion

4. Rank One Mixed Modules

5. Warfield Modules

Dimension in topological structures: Topological closure and local property

2. Closure

3. Local property

4. Some examples

On kernel modules of cotorsion pairs

2. Modules in the kernel

3. Applications to almost perfect domains

4. Weak-injective envelopes

5. Flat covers

References.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-9098-0