====== Permutation Group ======
====Definition==== 
A $\textdef{permutation group}$ on $X$ is a set of [[definition:permutation]]s of $X$ that contains the identity permutation and is closed under function composition and taking inverses.

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==== Remarks ==== 
  * Alternately, a permutation group is a subgroup of $\sym{X}$, where $\sym{X}$ denotes the [[definition:symmetric group]] on $X$.


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==== $\LaTeX$ version ====
<file tex definition.permutation_group.tex>
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% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}
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\begin{definition}
A \textdef{permutation group} on $X$ is a set of permutations of $X$ that contains the identity permutation and is closed under function composition and taking inverses.
\end{definition}
</file>

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


{{tag>definition needsreview rben ben rjosh}}