View source for Transposition (group theory)

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==Definition==
Let {{M|S_k}} denote the [[symmetric group]] on {{M|k\in\mathbb{N} }} symbols. Then:
* {{M|(i j)}} denotes (in ordinary {{link|cycle notation|group theory}} the permutation:
** {{M|(i j): i\mapsto j}}, {{M|(i j):j\mapsto i}} and for all other {{M|m\in\{1,\ldots,k\} }} (so {{M|m\ne i}} and {{M|m\ne j}}) we have: {{M|(i j):m\mapsto m}}
Such an {{M|(i j)}} is called a ''transposition''.
==See also==
* [[Every element of the symmetric group can be written as an even or odd number of transpositions, but not both]]
==References==
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{{Definition|Group Theory|Abstract Algebra}}