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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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]!

Counting quiver representations over finite fields via graph enumeration

It follows immediately from Cayley's theorem that dim [V.sub.n] = [(n + 1).sup.n-1].

Extending the parking space

Theorem: Cayley's theorem for Pre [A.sup.*]-algebras (Part-I)

Cayley's theorem for centre of Pre [A.sup.*]-algebras

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.