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.

• Alternately, a permutation group is a subgroup of $\sym{X}$, where $\sym{X}$ denotes the symmetric group on $X$.

definition.permutation_group.tex

%%%%%
% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}  \DeclareMathOperator{\sym}{Sym} 
%%%%%
\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}

• Permutation group

definition needsreview rben