Group Ring Groups. Volume 1, Orders and Generic Constructions of Units / Ángel del Río, Eric Jespers.

Format:

Book

Author/Creator:

Jespers, Eric, author.

del Río, Ángel, author.

Series:

De Gruyter graduate.

De Gruyter Textbook ; Volume 1

Language:

English

Subjects (All):

Group rings.

Rings (Algebra).

Physical Description:

1 online resource (460 pages) : illustrations.

Place of Publication:

Berlin ; Boston : De Gruyter, [2015]

Language Note:

English

Summary:

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Contents:

Frontmatter

Preface

Contents

1. Units in group rings: an introduction

2. Representations of algebras

3. Wedderburn decomposition of semisimple group algebras

4. Dedekind domains, valuations and orders

5. The group of units of an order

6. Cyclotomic integers

7. Central units

8. Generic units

9. K-theory

10. General linear groups of degree 2

11. Generators of the unit group of an integral group ring

12. Exceptional simple components

13. Idempotents and central units in group rings

References

Index of Notation

Index

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and indexes.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9783110372946

3110372940

9783110386172

3110386178

OCLC:

1013939619