Robert Wilson

The Finite Simple Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

The finite simple groups are the building blocks from which all the finite groups are made and as such they are objects of fundamental importance throughout mathematics. The classification of the finite simple groups was one of the great mathematical achievements of the twentieth century, yet these groups remain difficult to study which hinders applications of the classification.

This textbook brings the finite simple groups to life by giving concrete constructions of most of them, sufficient to illuminate their structure and permit real calculations both in the groups themselves and in the underlying geometrical or algebraic structures. This is the first time that all the finite simple groups have been treated together in this way and the book points out their connections, for example between exceptional behaviour of generic groups and the existence of sporadic groups, and discusses a number of new approaches to some of the groups. Many exercises of varying difficulty are provided.

The Finite Simple Groups is aimed at advanced undergraduate and graduate students in algebra as well as professional mathematicians and scientists who use groups and want to apply the knowledge which the classification has given us. The main prerequisite is an undergraduate course in group theory up to the level of Sylow's theorems.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 298
• Erscheinungstermin: 12. Dezember 2009
• Englisch
• ISBN-13: 9781848009882
• Artikelnr.: 37338326

Autorenporträt

Robert A. Wilson wurde geboren am 18. Januar 1932 in New York, studierte Mathematik, Elektrotechnik, Englisch, Pädagogik und graduierte schließlich in Psychologie. Nach diversen Jobs, unter anderem als Mitarbeiter von 'Playboy', wurde er Vizepräsident des Institute for the Study of Human Future in Berkeley.

Inhaltsangabe

The alternating groups.- The classical groups.- The exceptional groups.- The sporadic groups.

Rezensionen

From the reviews: "The book under review has as its main goal to give an introductory overview of the construction and main properties of all finite simple groups. ... This book is the first one that attempts to give a systematic treatment of all finite simple groups, using the more recent and efficient constructions ... . The author succeeds in making this important but difficult area of mathematics readily accessible to a large sector of the mathematical community, and for this we should be grateful." (Felipe Zaldivar, The Mathematical Association of America, March, 2010) "One of the great achievements of mathematics was the classification of the finite simple groups ... . the book brings much information to the classroom. It contains exactly those things one would like to know if one were to meet the individual simple groups for the first time. ... perfectly suitable for an advanced course or seminar. ... accessible also to those who are not great experts in group theory. Anyone interested in finite groups ... should have this book on his or her bookshelf." (Gernot Stroth, Mathematical Reviews, Issue 2011 e)