Diameter (group theory)

In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity.
Consider a finite group, and any set of generators. Define to be the graph diameter of the Cayley graph. Then the diameter of is the largest value of taken over all generating sets.
For instance, every finite cyclic group of order, the Cayley graph for a generating set with one generator is an -vertex cycle graph. The diameter of this graph, and of the group, is.
It is conjectured, for all non-abelian finite simple groups, that
Many partial results are known but the full conjecture remains open.