| 12 Jan – 23 Jan |
Amos Turchet & Laura Capuano |
Introduction to Groups
- Basic Axioms and Examples,
- Dihedral Groups,
- Symmetric Groups,
- Matrix Groups,
- The Quaternion Group,
- Homomorphisms and Isomorphisms,
- Group Actions
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| 26 Jan – 6 Feb |
Francesco Campagna & Peter Stevenhagen
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Subgroups
- Definition and Examples,
- Centralizers and Normalizers,
- Stabilizers and Kernels,
- Cyclic Groups and Cyclic Subgroups,
- Subgroups Generated by Subsets of a Group,
- The Lattice of Subgroups of a Group
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| 9 Feb – 20 Feb |
Valerio Talamanca & A. El-Guindy |
Quotient Groups and Homomorphisms
- Definitions and Examples,
- More on Cosets and Lagrange's Theorem,
- The Isomorphism Theorems,
- Composition Series and the Holder Program,
- Transpositions and the Alternating Group
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MIDTERM EXAM |
| 6 Apr – 17 Apr |
Laura Geatti & Lea Terracini |
Group Actions
- Group Actions and Permutation Representations,
- Groups Acting on Themselves by Left Multiplication-Cayley's Theorem,
- Groups Acting on Themselves by Conjugation--The Class Equation,
- Automorphisms,
- The Sylow Theorems,
- The Simplicity of An
|
| 20 Apr – 1 May |
Francesco Pappalardi |
Direct and Semidirect Products and Abelian Groups
- Direct Products,
- The Fundamental Theorem of Finitely Generated Abelian Groups,
- Table of Groups of Small Order,
- Recognizing Direct Products,
- Semidirect Products
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| 4 May – 15 May |
Rashid Zaare-Nahandi & Rahim Zaare-Nahandi |
Further Topics in Group Theory
- p-groups,
- Nilpotent Groups and Solvable Groups,
- Applications in Groups of Medium Order
- Free Groups
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