Cayley's theorem


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Cayley's theorem

[′kā‚lēz ‚thir·əm]
(mathematics)
A theorem that any group G is isomorphic to a subgroup of the group of permutations on G.
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It follows immediately from Cayley's theorem that dim [V.
Extending the parking space
alpha]-2] is the number of trees on [alpha] labeled vertices by Cayley's Theorem.
Counting quiver representations over finite fields via graph enumeration
He takes a modern, geometric approach to group theory, which is particularly useful in the study of infinite groups, focusing on Cayley's theorems first, including his basic theorem, the symmetry groups of graphs, or bits and stabilizers, generating sets and Cayley graphs, fundamental domains and generating sets, and words and paths.
Groups, graphs, and trees; an introduction to the geometry of infinite groups

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