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 $\backslash left(G,\backslash circ\backslash right)$, and any set of generators . Define $D\_S$ to be the graph diameter of the Cayley graph $\backslash Lambda=\backslash left(G,S\backslash right)$. Then the diameter of $\backslash left(G,\backslash circ\backslash right)$ is the largest value of $D\_S$ 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 $\backslash lfloor\; s/2\backslash rfloor$.
It is conjectured, for all non-abelian finite simple groups , that
:$\backslash operatorname(G)\; \backslash leqslant\; \backslash left(\backslash log|G|\backslash right)^.$
Many partial results are known but the full conjecture remains open..

References

Category:Finite groups Category:Measures of complexity {{math-stub

References

Category:Finite groups Category:Measures of complexity {{math-stub