Wednesday 27 February 2013 h. 15:00, room 2BC30

Martino GARONZI (Dip. Mat.)

"Ideas in finite group theory"

-Abstract

In this talk I will present the basic ideas of finite group theory, which was invented by Evariste Galois to study polynomials. I will show how finite groups and polynomials interact. I will talk about the properties of the Symmetric group, which is one of the foundamental objects of the theory. I will illustrate the main elementary results of finite group theory (the theorems of Lagrange, Cauchy, Cayley and Sylow) with many examples and I will outline how problems are usually dealt with. I will introduce abelian, nilpotent, solvable and non-solvable groups with many examples. Then, I will present the specific problem I dealt with in my Ph.D thesis, the covering problem. Many examples will be given. If there is time, I will use not more than ten minutes to state some results I obtained in my thesis.

Rif. int. C. Marastoni, T. Vargiolu