Dr. Rachel Camina (Cambridge).
29th November 2005

Conjugacy class sizes and the IP-graph.

Abstract: In 1989 Bertram, Herzog and Mann introduced the following graph, Gamma, attached to a finite group G. Let the vertices of Gamma be the non-central conjugacy classes of G and link 2 conjugacy classes C and D if the orders |C| and |D| are not coprime. The authors proved various structural results about Gamma. In 1993 Isaacs and Praeger introduced a generalisation of Gamma, now known as the IP-graph. We consider the proofs of Bertram, Herzog and Mann and see if they can be extended to cover the IP-graph.