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

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