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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-07-04 and was most recently seen on 2026-07-04.
In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of a symmetric group.
More specifically, G is isomorphic to a subgroup of the symmetric group whose elements are the permutations of the underlying set of G.
Explicitly,for each , the left-multiplication-by-g map sending each element x to gx is a permutation of G, and
the map sending each element g to is an injective homomorphism, so it defines an isomorphism from G onto a subgroup of .
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