Polynomial Invariants of Finite Groups

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Written by an algebraic topologist motivated by his own desire to learn, this well-written book represents the compilation of the most essential and interesting results and methods in the theory of polynomial invariants of finite groups. From the table of contents: - Invariants and Relative Invariants - Finite Generation of Invariants - Construction of Invariants - Poincaré Series - Dimension Theoretic Properties of Rings of Invariants - Homological Properties of Invariants - Groups Generated by Reflections - Modular Invariants - Polynomial Tensor Exterior Algebras - Invariant Theory and Algebraic Topology - The Steenrod Algebra and Modular Invariant Theory

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Editorial Reviews

An algebraic topologist explores the invariant theory of finite groups, confining himself to finite groups and polynomial invariants in order to keep the volume liftable by a single mathematician. A recurrent theme is the extension of characteristic zero results to arbitrary characteristics, or to at least the nonmodular case, and the interest at finding many of the extensions false. Poincare series, dimensional theoretic properties of rings of invariants, and polynomial tensor exterior algebras are among the topics. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Meet the Author

Larry Smith
Larry Smith

SMITH Magazine founding editor Larry Smith has worked as an editor at Men's Journal, ESPN: The Magazine, and Might. His writing has appeared in the New York Times, the Los Angeles Times, Popular Science, on Salon.com, and many other places. Larry lives in New York City

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Table of Contents

1 Invariants and Relative Invariants 1
2 Finite Generation of Invariants 24
3 Construction of Invariants 41
4 Poincare Series 74
5 Dimension Theoretic Properties of Rings of Invariants 105
6 Homological Properties of Invariants 140
7 Groups Generated by Reflections 177
8 Modular Invariants 236
9 Polynomial Tensor Exterior Algebras 265
10 Invariant Theory and Algebraic Topology 285
11 The Steenrod Algebra and Modular Invariant Theory 323
References 341
Notations 355
Index 357
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