Difference between revisions of "Symmetric group"
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| − | The '''symmetric group''' <math>S_{n}</math> is defined to be the group of all | + | The '''symmetric group''' <math>S_{n}</math> is defined to be the [[group]] of all [[permutation]]s of <math>n</math> objects. |
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| + | Knowledge of the general symmetric group <math>S_{n}</math> is crucial in such areas as [[Galois Theory]], including proving that [[polynomial]] [[equation]]s of degree five and higher are unsolvable through the use of elementary arithmetic and root extractions. | ||
Revision as of 21:04, 13 March 2008
The symmetric group 
is defined to be the group of all permutations of 
objects.
Knowledge of the general symmetric group is crucial in such areas as Galois Theory, including proving that polynomial equations of degree five and higher are unsolvable through the use of elementary arithmetic and root extractions.
