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 S. Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of 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 .^{[1]}

It is conjectured, for all non-abelian finite simple groups G, that^{[2]}

Many partial results are known but the full conjecture remains open.^{[3]}

## References

**^**Babai, László; Seress, Ákos (1992), "On the diameter of permutation groups",*European Journal of Combinatorics*,**13**(4): 231–243, arXiv:1109.3550, doi:10.1016/S0195-6698(05)80029-0, MR 1179520.**^**Babai & Seress (1992), Conj. 1.7. This conjecture is misquoted by Helfgott & Seress (2014), who omit the non-abelian qualifier.**^**Helfgott, Harald A.; Seress, Ákos (2014), "On the diameter of permutation groups",*Annals of Mathematics*, Second Series,**179**(2): 611–658, arXiv:1109.3550, doi:10.4007/annals.2014.179.2.4, MR 3152942.