دانلود کتاب Cohomology of finite groups

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Introduction
Chapter I. Group Extensions, SimpleAigebras and Cohomology
0. Introduction
1. Group Extensions
2. Extensions Associated to the Quaternions
3. Central Extensions and S^1 Bundles on the Torus T^2
4. The PuIl-back Construction and Extensions
5. The Obstruction to Extension When the Center Is Non-Trivial
6. Counting the Number of Extensions
7. The Relation Satisfied by μ(g_1, g_2, g_3)
8. Associative Algebras and H^2_Φ (G; C)
Chapter II. Classifying Spaces and Group Cohomology
0. Introduction
1. Preliminaries on Classifying Spaces
2. Eilenberg-MacLane Spaces and the Steenrod Algebra A(p)
3. Group Cohomology
4. Cup Products
5. Restrietion and Transfer
6. The Cartan-Eilenberg Double Coset Formula
7. Tate Cohomology and Applications
8. The First Cohomology Group and Out(G)
Chapter III. Modular Invariant Theory
0. Introduction
1. General Invariants
2. The Dickson Algebra
3. A Theorem of Serre
4. The Invariants in H*((Z/p)^n; F_p) Under the Action of S_n
5. The Cardenas-Kuhn Theorem
6. Discussion of Related Topics and Further Results
Chapter IV. Spectral Sequences and Detection Theorems
0. Introduction
1. The Lyndon-Hochschild-Serre Spectral Sequence: Geometric Approach
2. Change of Rings and the Lyndon-Hochschild-Serre Spectral Sequence
3. Chain Approximations in Acyclic Complexes
4. Groups With Cohomology Detected by Abelian Subgroups
5. Structure Theorems for the Ring H*(G; F_p)
6. The Classification and Cohomology Rings of Periodic Groups
7. The Definition and Properties of Steenrod Squares
Chapter V. G-Complexes and Equivariant Cohomology
0. Introduction to Cohomological Methods
1. Restrietions on Group Actions
2. General Properties of Posets Associated to Finite Groups
3. Applications to Cohomology
Chapter VI. The Cohomology of Symmetric Groups
0. Introduction
1. Detection Theorems for H*(S_n; F_p) and Construction of Generators
2. Hopf Aigebras
3. The Structure of H_*(S_n; F_p)
4. More Invariant Theory
5. H*(S_n), n = 6, 8, 10, 12
6. The Cohomology of the Alternating Groups
Chapter VII. Finite Groups of Lie Type
1. Preliminary Remarks
2. The Classical Groups of Lie Type
3. The Orders of the Finite Orthogonal and Symplectic Groups
4. The Cohomology of the Groups GL_n(q)
5. The Cohomology of the Groups O^*_n(q) for q Odd
6. The Groups H*(Sp_{2n}(q); F_2)
7. The Exceptional Chevalley Groups
Chapter VIII. Cohomology of Sporadic Simple Groups
0. Introduction
1. The Cohomology of M_{11}
2. The Cohomology of J_1
3. The Cohomology of M_{12}
4. Discussion of H*(M_{12}; F_2)
5. The Cohomology of Other Sporadic Simple Groups
Chapter IX. The Plus Construction and Applications
0. Preliminaries
1. Definitions
2. Classification and Construction of Acyclic Maps
3. Examples and Applications
4. The Kan-Thurston Theorem
Chapter X. The Schur Subgroup of the Brauer Group
0. Introduction
1. The Brauer Groups of Complete Local Fields
2. The Brauer Group and the Schur Subgroup for Finite Extensions of Q
3. The Explicit Generators of the Schur Subgroup
4. The Groups H^*_{cont}(G_F; Q/Z) and H_{cont}(G_v; Q/Z}
5. The Explicit Structure of the Schur Subgroup, S(F)
References
Index