The Structure of Groups With Complete Common Divisor Graphs

Let G be a nite group, and write cd(G) for the set of degrees of irreducible characters of G. We de ne (G) to be the graph whose vertex set is cd(G) − {1}, and there is an edgebetween a and b if (a; b) > 1. We prove that if (G) is a complete graph, then G is a solvable group.

Keywords:

Character degree , Solvable groups , Common-divisor character degree graphs