A Course in Group Theory / Edition 1

A Course in Group Theory / Edition 1

by John F. Humphreys
     
 


The classification of the finite simple groups is one of the major intellectual achievements of this century, but it remains almost completely unknown outside of the mathematics community. This introduction to group theory is also an attempt to make this important work better known. Emphasizing classification themes throughout, the book gives a clear and… See more details below

Overview


The classification of the finite simple groups is one of the major intellectual achievements of this century, but it remains almost completely unknown outside of the mathematics community. This introduction to group theory is also an attempt to make this important work better known. Emphasizing classification themes throughout, the book gives a clear and comprehensive introduction to groups and covers all topics likely to be encountered in an undergraduate course. Introductory chapters explain the concepts of group, subgroup and normal subgroup, and quotient group. The homomorphism and isomorphism theorems are explained, along with an introduction to G-sets. Subsequent chapters deal with finite abelian groups, the Jordan-Holder theorem, soluble groups, p-groups, and group extensions. The numerous worked examples and exercises in this excellent and self-contained introduction will also encourage undergraduates (and first year graduates) to further study.

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Product Details

ISBN-13:
9780198534594
Publisher:
Oxford University Press, USA
Publication date:
04/28/1996
Edition description:
New Edition
Pages:
296
Sales rank:
1,088,372
Product dimensions:
9.32(w) x 6.19(h) x 0.61(d)

Table of Contents

1Definitions and examples1
2Maps and relations on sets8
3Elementary consequences of the definitions18
4Subgroups30
5Cosets and Lagrange's Theorem38
6Error-correcting codes49
7Normal subgroups and quotient groups59
8The Homomorphism Theorem68
9Permutations77
10The Orbit-Stabiliser Theorem89
11The Sylow Theorems98
12Applications of Sylow theory106
13Direct products112
14The classification of finite abelian groups120
15The Jordan-Holder Theorem128
16Composition factors and chief factors137
17Soluble groups146
18Examples of soluble groups155
19Semidirect products and wreath products163
20Extensions174
21Central and cyclic extensions183
22Groups with at most 31 elements192
23The projective special linear groups202
24The Mathieu groups213
25The classification of finite simple groups222
A Prerequisites from number theory and linear algebra234
B Groups of order < 32238
C Solutions to exercises243
Bibliography275
Index277

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