Symmetric group
Revision as of 15:10, 14 March 2008 by Lowtopology (talk | contribs)
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. An important theorem in Galois Theory is that the Galois group of the general polynomial equation of degree is .
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