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

26 Jan – 6 Feb 
Francesco Campagna & Peter Stevenhagen

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

9 Feb – 20 Feb 
Valerio Talamanca & A. ElGuindy 
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

MIDTERM EXAM 
6 Apr – 17 Apr 
Laura Geatti & Lea Terracini 
Group Actions
 Group Actions and Permutation Representations,
 Groups Acting on Themselves by Left MultiplicationCayley's Theorem,
 Groups Acting on Themselves by ConjugationThe Class Equation,
 Automorphisms,
 The Sylow Theorems,
 The Simplicity of A_{n}

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

4 May – 15 May 
Rashid ZaareNahandi & Rahim ZaareNahandi 
Further Topics in Group Theory
 pgroups,
 Nilpotent Groups and Solvable Groups,
 Applications in Groups of Medium Order
 Free Groups

