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permutation group (Definition)

A permutation group is a pair $ (G,X)$ where $ G$ is an abstract group, and $ X$ is a set on which $ G$ acts faithfully. Alternatively, this can be thought of as a group $ G$ equipped with a homomorphism in to $ \mathrm{Sym}(X)$, the symmetric group on $ X$.



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Cross-references: symmetric group, homomorphism, faithfully, group
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This is version 2 of permutation group, born on 2002-12-14, modified 2003-08-22.
Object id is 3758, canonical name is PermutationGroup2.
Accessed 4597 times total.

Classification:
AMS MSC: 20B05 (Group theory and generalizations :: Permutation groups :: General theory for finite groups)
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