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.
References in periodicals archive ?
But [G.sup.[alpha].sub.[alpha]-1] is just the number of (spanning) trees on [alpha] labeled vertices, which is [[alpha].sup.[alpha]-2] by Cayley's Theorem. So the leading coefficient is [2.sup.[alpha]-1] [[alpha].sup.[alpha]-2]/[alpha]!
It follows immediately from Cayley's theorem that dim [V.sub.n] = [(n + 1).sup.n-1].
Theorem: Cayley's theorem for Pre [A.sup.*]-algebras (Part-I)
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.