Bounding graph diameters of nonsolvable groups

Associated with the character degrees of a finite group is the common-divisor graph, where the nontrivial degrees are the vertices and distinct degrees are adjacent when they have a common nontrivial divisor. The author has shown that common-divisor graphs for solvable groups have diameters of at most 3. The present paper extends this result to nonsolvable groups by showing that their common-divisor graphs also have diameters bounded above by 3.