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 . Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of 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 ..
It is conjectured, for all non-abelian finite simple groups , that, Conj. 1.7. This conjecture is misquoted by , who omit the non-abelian qualifier.
Many partial results are known but the full conjecture remains open..
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