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(G,\circ\right), and any set of generators . Define D_S to be the graph diameter of the Cayley graph \Lambda=\left(G,S\right). Then the diameter of \left(G,\circ\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(G) \leqslant \left(\log|G|\right)^. Many partial results are known but the full conjecture remains open..


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