The Finite Simple Groups: 251 (Graduate Texts in Mathematics, 251) - Tapa dura

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9781848009875: The Finite Simple Groups: 251 (Graduate Texts in Mathematics, 251)
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ISBN 10: 1848009879 ISBN 13: 9781848009875
Editorial: Springer, 2009

Sinopsis

Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].

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De la contraportada

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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Editorial
Springer
Año de publicación
2009
Idioma
Inglés
ISBN 10 
1848009879
ISBN 13 
9781848009875
Encuadernación
Tapa dura
Número de páginas
316
Contacto del fabricante
no disponible
Persona responsable
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Friedrich-Karl-Str. 9
Hamburg
Alemania

Otras ediciones populares con el mismo título

9781447125273: The Finite Simple Groups: 251 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  1447125274 ISBN 13:  9781447125273
Editorial: Springer, 2012
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