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permutation group
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(Definition)
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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 $\Sym (X)$ , the symmetric group on $X$ .
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"permutation group" is owned by bwebste.
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Cross-references: symmetric group, homomorphism, faithfully, group
There are 20 references to this entry.
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 5733 times total.
Classification:
| AMS MSC: | 20B05 (Group theory and generalizations :: Permutation groups :: General theory for finite groups) |
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Pending Errata and Addenda
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