Table of Contents

The Composition Of Permutations Is A Permutation

Theorem

Let be a set. Suppose that are all Permutation of . Then the composition is a permutation of .

Remarks

$\LaTeX$ version

theorem.the_composition_of_permutations_is_a_permutation.tex
%%%%%
% DEPENDENCIES 
% RequiredMacros: \DeclareMathOperator{\syl}{Syl} 
%%%%%
\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}