A graph related to conjugacy classes of solvable groups
Consider the graph \(\Gamma^* (G)\) related to the finite group \(G\) defined so that its vertices are the prime divisors of the sizes of conjugacy classes and two vertices are connected if they both divide the size of some conjugacy class. The author then considers two subgroups, induced respectively on the set of primes \(p\) for which the normalizer Sylow \(p\)-group is the centralizer and those primes for which it is not. He proves that these two graphs are complete for soluble groups unless they contain a section with a very specific structure.
scientific article; zbMATH DE number 815923