====== The Composition Of Permutations Is A Permutation ======
====Theorem==== 
Let $X$ be a set. Suppose that $\sigma_1, \sigma_2, \ldots,\sigma_k$ are all [[definition:Permutation]] of $X$.  Then the composition 
$\sigma_1\circ \sigma_2\circ \ldots\circ \sigma_k$
is a permutation of $X$.


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==== Remarks ==== 
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==== $\LaTeX$ version ====
<file tex theorem.the_composition_of_permutations_is_a_permutation.tex>
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% DEPENDENCIES 
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\begin{theorem}
Let $X$ be a set. Suppose that $\sigma_1, \sigma_2, \ldots,\sigma_k$ are all [[Definition.Permutation|permutations]] of $X$.  Then the composition 
$\sigma_1\circ \sigma_2\circ \ldots\circ \sigma_k$
is a permutation of $X$.
\end{theorem}
</file>

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==== External links ====
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{{tag>theorem}}