View source for Example:Permutation (group theory) of S5/Body

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==Example body==
</noinclude>Let us consider {{M|S_5}} as an example.
* Let {{M|\sigma\in S_5}} be the permutation given as follows:
** {{M|\sigma:1\mapsto 3}}, {{M|\sigma:2\mapsto 2}}, {{M|\sigma:3\mapsto 5}}, {{M|\sigma:4\mapsto 1}}, {{M|\sigma:5\mapsto 4}}
*: This can be written more neatly as:
** {{MM|1=\left(\begin{array}{ccccc}1 & 2 & 3 & 4 & 5 \\ 3 & 2 & 5 & 1 & 4\end{array}\right) }}, the thing in the top row is sent to the thing below it. 
*** This can be written as the product of disjoint cycles too:
**** {{MM|1=(1\ 3\ 5\ 4)}} or {{M|1=(1\ 3\ 5\ 4)(2)}} if you do not take the "implicit identity" part. That is any element not in a cycle stays the same
*** Or as {{link|transposition|group theory|s}}
**** {{MM|1=(1\ 4)(1\ 5)(1\ 3)}} - recall we read right-to-left, so this is read:
***** {{M|1\mapsto 3\mapsto 3\mapsto 3}}
***** {{M|3\mapsto 1\mapsto 5\mapsto 5}}
***** {{M|5\mapsto 5\mapsto 1\mapsto 4}}
***** {{M|4\mapsto 4\mapsto 4\mapsto 1}} - the cycle {{M|(1\ 3\ 5\ 4)}}
***** And of course {{M|2\mapsto 2\mapsto 2\mapsto 2}}<noinclude>
==Notes==
<references group="Note"/>
{{Example Of|Abstract Algebra|Group Theory}}
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