About: Diameter (group theory)

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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 , and any set of generators S. Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of 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 . It is conjectured, for all non-abelian finite simple groups G, that

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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 , and any set of generators S. Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of 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 . It is conjectured, for all non-abelian finite simple groups G, that Many partial results are known but the full conjecture remains open. (en)
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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 , and any set of generators S. Define to be the graph diameter of the Cayley graph . Then the diameter of is the largest value of 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 . It is conjectured, for all non-abelian finite simple groups G, that (en)
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  • Diameter (group theory) (en)
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