Diameter of a finite group

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 ( G , ∘ ) , and any set of generators S. Define D S to be the graph diameter of the Cayley graph Λ = ( G , S ) . Then the diameter of ( G , ∘ ) is the largest value of D S taken over all generating sets S.

For instance, every finite cyclic group of order s, the Cayley graph for a generating set with one generator is an s-vertex cycle graph. The diameter of this graph, and of the group, is ⌊ s / 2 ⌋ .

It is conjectured, for all non-abelian finite simple groups G, that

Many partial results are known but the full conjecture remains open.