====== Symmetric Group ======
====Definition==== 
Let $X$ be any set. The $\textdef{symmetric group}$ on $X$, denoted $\sym(X)$, is the set of all [[permutation]]s of $X$. We denote by $S_n$ the symmetric group on $X = \{1,2,\ldots, n\}$.


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==== Remarks ==== 
  * None.


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==== $\LaTeX$ version ====
<file tex definition.symmetric_group.tex>
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% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}  \DeclareMathOperator{\sym}{Sym} 
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\begin{definition}
Let $X$ be any set. The \textdef{symmetric group} on $X$, denoted $\sym(X)$, is the set of all permutations of $X$. We denote by $S_n$ the symmetric group on $X = \{1,2,\ldots, n\}$.
\end{definition}
</file>

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==== External links ====
  * [[wp>Symmetric group]]


{{tag>definition needsreview rjosh rben ben}}