Polynomial Invariants of Finite Groups

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

1. Invariants and Relative Invariants 2. Finite Generation of Invariants 3. Construction of Invariants 4. Poincare Series 5. Dimension Theoretic Properties of Rings of Invariants 6. Homological Properties of Invariants 7. Groups Generated by Reflections 8. Modular Invariants 9. Polynomial Tensor Exterior Algebras 10. Invariant Theory and Algebraic Topology 11. The Steenrod Algebra and Modular Invariant Theory

Professional Practice & Development

Larry Smith

This book represents the compilation of the most essential and interesting results in the theory of polynomial invariants of finite groups. It also introduces some of the basic concepts behind ideal theory and homological algebra in a liberating context and discusses the mutual impact of invariant theory and algebraic topology. Along the way, the author examines such topics as the Hilbert-Noether finiteness theorems, methods for constructing invariants, the Poincaré series, localization and use of gradings, the Hilbert Syzygy theorem. He includes numerous examples and illustrates the theorems by applying them to concrete cases.