Alphabeta MathBlocks Defect Groups and the Brauer Homomorphism — Examples
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Chain Conditions, Semisimple Modules and the Wedderburn–Artin Theorem
- Cosets, Index and Lagrange's Theorem
- Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Actions, Orbits, Stabilisers and Cayley's Theorem
- Group Homomorphisms and the Isomorphism Theorems
- Ideals, Quotient Rings and the Isomorphism Theorems for Rings
- Induced Representations, Frobenius Reciprocity and Applications
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Polynomial Rings, the Division Algorithm and Roots
- Rings, Subrings, Integral Domains and Fields
- Sylow's Theorems, p-Groups and Nilpotent Groups
- Tensor Products of Modules
- The Group Algebra and Representations of Finite Groups
Commutative Algebra
Group Theory
Linear Algebra
Number Theory
Real Analysis
Representation Theory of Groups
2 · Logical flowchart
3 · Items
Example
Defect and Brauer pairs for a4 in characteristic three
Example
Brauer pair branching for C₃ ⋊ D₈ in characteristic two
Example
Blocks and defect groups of s3
Example
Defect zero and p group boundaries
Sources
- Jacobsen, Block fusion systems and the center of the group ring, Example 2.12; coefficients and primitivity verified above
- Original example; order criterion from AKO, Fusion Systems in Algebra and Topology, IV §2 Theorem 2.10; all group and algebra calculations supplied here
- Webb, A Course in Finite Group Representation Theory, §§11.3, 11.6 and 12.3–12.5, especially pp.240–245