Resumen de On the vanishing prime graph of finite groups

Silvio Dolfi , Emanuele Pacifici , Lucía Sanus Vitoria , Pablo Spiga

• Let G be a finite group. An element g �¸ G is called a vanishing element of G if there exists an irreducible complex character �Ô of G such that �Ô(g) = 0. In this paper we study the vanishing prime graph �¡(G), whose vertices are the prime numbers dividing the orders of some vanishing element of G, and two distinct vertices p and q are adjacent if and only if G has a vanishing element of order divisible by pq. Among other things we prove that, similarly to what holds for the prime graph of G, the graph �¡(G) has at most six connected components.