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
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 group
s , that
Many partial results are known but the full conjecture remains open.
Category:Measures of complexity