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.