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A Course on Finite Groups (Universitext)
Synopses & Reviews
A Course on Finite Groups introduces the fundamentals of group theory to advanced undergraduate and beginning graduate students. Based on a series of lecture courses developed by the author over many years, the book starts with the basic definitions and examples and develops the theory to the point where a number of classic theorems can be proved. The topics covered include: group constructions; homomorphisms and isomorphisms; actions; Sylow theory; products and Abelian groups; series; nilpotent and soluble groups; and an introduction to the classification of the finite simple groups. A number of groups are described in detail and the reader is encouraged to work with one of the many computer algebra packages available to construct and experience "actual" groups for themselves in order to develop a deeper understanding of the theory and the significance of the theorems. Numerous problems, of varying levels of difficulty, help to test understanding. A brief resumé of the basic set theory and number theory required for the text is provided in an appendix, and a wealth of extra resources is available online at www.springer.com, including: hints and/or full solutions to all of the exercises; extension material for many of the chapters, covering more challenging topics and results for further study; and two additional chapters providing an introduction to group representation theory.
Group Theory is a topic that has wide-ranging uses in the field of mathematics. Despite this, the only books still available on the market today are either too basic or too advanced for most European studying at the undergraduate level. This became apparent to Dr. Harvey Rose whilst he was lecturing at Bristol University, which led to the creation of this book, based upon Rose's own lecture notes and years of expertise.
Aimed primarily at being a textbook for universities in the UK and mainland Europe, Rosea (TM)s book begins with the basic definitions and moves on to develop the theory, using examples to help students with their understanding. Dr. Rose offers a comprehensive account of the finite groups, this work being based upon his many years as a lecturer in the subject, although some of the early material within the book can be applied to both finite and infinite cases.
Group Theory has wide-ranging uses in the field of mathematics. This book offers a comprehensive account of the finite groups. It begins with the basic definitions and moves on to develop the theory, using examples to help students with their understanding.
Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
Table of Contents
The Group Concept.- Elementary Group Properties.- Group Construction and Representation.- Homomorphisms.- Action and the Orbit-Stabiliser Theorem.- p-Groups and Sylow Theory.- Products and Abelian Groups.- Groups of Order 24, Three Examples.- Series, Jordan Hölder Theorem and the Extension Problem.- Nilpotency.- Solubility.- Simple Groups of Order Less Than 10000.- Representation and Character Theory.- Character Tables and Theorems of Burnside and Frobenius.- Appendices.
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