Representations and Characters of Groups

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Cambridge University Press, Oct 18, 2001 - Mathematics - 458 pages
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This is the second edition of the popular textbook on representation theory of finite groups. The authors have revised the text greatly and included new chapters on Characters of GL(2,q) and Permutations and Characters. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book.
  

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This is the best book to know what "Representation" actually means....

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Simple and Excellent book on representations of groups

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Contents

Groups and homomorphisms
1
Vector spaces and linear transformations
14
Group representations
30
FGmodules
38
FGsubmodules and reducibility
49
Group algebras
53
FGhomomorphisms
61
Maschkes Theorem
70
Tensor products
188
Restriction to a subgroup
210
Induced modules and characters
224
Algebraic integers
244
Real representations
263
Summary of properties of character tables
283
Characters of groups of order pq
288
Characters of some pgroups
298

Schurs Lemma
78
Irreducible modules and the group algebra
89
More on the group algebra
95
Conjugacy classes
104
Characters
117
Inner products of characters
133
The number of irreducible characters
152
Character tables and orthogonality relations
159
Normal subgroups and lifted characters
168
Some elementary character tables
179
Character table of the simple group of order 168
311
Character table of GL2 q
322
Permutations and characters
337
Applications to group theory
348
Burnsides Theorem
361
An application of representation theory to molecular vibration
367
Solutions to exercises
397
Bibliography
454
Index
455
Copyright

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Multilinear Algebra
Russell Merris
Limited preview - 1997
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