Difference between revisions of "Symmetric group"
Lowtopology (talk | contribs) |
Lowtopology (talk | contribs) |
||
| Line 1: | Line 1: | ||
| − | The '''symmetric group''' <math>S_{n}</math> is defined to be the group of all permutations of <math>n</math> objects. | + | The '''symmetric group''' <math>S_{n}</math> is defined to be the group of all permutations of <math>n</math> objects. Knowledge of the general symmetric group $S_{n} is crucial in such areas as [[Galois Theory]], including proving that equations of degree 5 and higher are unsolvable through the use of elementary arithmetic and root extractions. |
| − | |||
| − | |||
| − | { | ||
Revision as of 19:42, 13 March 2008
The symmetric group 
is defined to be the group of all permutations of 
objects. Knowledge of the general symmetric group $S_{n} is crucial in such areas as Galois Theory, including proving that equations of degree 5 and higher are unsolvable through the use of elementary arithmetic and root extractions.
