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 formula_1, and any set of generators . Define formula_2 to be the graph diameter of the Cayley graph formula_3. Then the diameter of formula_1 is the largest value of formula_2 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 formula_6.
It is conjectured, for all non-abelian finite simple groups , that
Many partial results are known but the full conjecture remains open.