Diameter (group theory)

In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity.

, and any set of generators S. Define

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.

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