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In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation…
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group permutation set permutations groups elements action composition given element product two identity first symmetric order square written notation example
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Permutation group | is a | group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G | 0.90 | text |
| Permutation group | is a | subgroup of a symmetric group | 0.90 | text |
| Permutation group | related to Basic properties and terminology | It | 0.60 | section |
| Permutation group | related to Basic properties and terminology | The | 0.60 | section |
| Permutation group | related to Basic properties and terminology | By Lagrange's | 0.60 | section |
| Permutation group | related to Basic properties and terminology | Sn | 0.60 | section |
| Permutation group | related to Cayley's theorem | Any | 0.60 | section |
| Permutation group | related to Cayley's theorem | In | 0.60 | section |
| Permutation group | related to Cayley's theorem | That | 0.60 | section |
| Permutation group | related to Cayley's theorem | For | 0.60 | section |
| Permutation group | related to Cayley's theorem | Each | 0.60 | section |
| Permutation group | related to Cayley's theorem | Cayley's | 0.60 | section |
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