SEMINAR: Groups and Combinatorics Seminar: On the vanishing graph of finite groups

Groups and Combinatorics Seminar

Pablo Spiga (UWA)

will speak

On the vanishing graph of finite groups

at 12 noon Tuesday 3rd of May in MLR2

Abstract: In this talk, we investigate a graph Gamma encoding some information on the zeros of the irreducible complex characters of a finite group G. (We say that the element g of G is a zero, if there exists an irreducible complex character $ hi$ with $ hi(g)=0$.) This graph Gamma is called "the vanishing graph" of G. The vertices of Gamma are the primes p such that G contains a zero whose order is divisible by p. Moreover, the edges of Gamma are the pairs {p,q} such that G contains a zero whose order is divisible by pq.

Clearly, Gamma is a subgraph of the prime graph. In this talk, we study the density of the graph Gamma and we show how some geometrical properties of Gamma generalise two classical character theory results of Thompson and of Ito-Michler.