On the diameter of a p-regular conjugacy class graph of finite groups II

摘要

Let G be a finite p-solvable group. Let us consider the graph Gamma(p)*(G) whose vertices are the primes which Occur as the divisors of the conjugacy classes of p-regular elements of G and two primes are joined by an edge if there exists such a class whose size is divisible by both primes. Suppose that Gamma(p)*(G) is a connected graph, then we prove that the diameter of this graph is at most 3 and this is the best bound. [References: 7]