**Seminario Teoría de grupos 12/05**

11:30 Aula Naranja ICMAT

Speaker: Victor Sotomayor (Centro Universitario EDEM, Valencia)

Title: On the class size prime graph of finite groups

Abstract: Let $G$ be a finite group, and $cs(G)$ be the set of its conjugacy class sizes. Many researchers in the literature have shown the in-depth relationship that exists between the arithmetical properties of $cs(G)$ and the structure of $G$. In the last decades, the use of the emph{class size prime graph} is gaining an increasing interest. This (simple undirected) graph has the prime divisors of the numbers in $cs(G)$ as set of vertices, and the edges are pairs ${p, q}$ such that $pq$ divides some number in $cs(G)$.

The aim of this talk is to present some current results, obtained in joint work with S. Dolfi, E. Pacifici and L. Sanus, about this subject.