Let $X$ be any set. A $\textdef{permutation group}$ on $X$ is any subgroup of $\sym{X}$; that is, it is a subset of $\sym{X}$ that contains the identity and is closed under composition and taking inverses.

• $\sym{X}$ denotes the symmetric group on $X$.

definition.permutation_group.tex

%%%%%
% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}  \DeclareMathOperator{\sym}{Sym} 
%%%%%
\begin{definition}
Let $X$ be any set. A \textdef{permutation group} on $X$ is any subgroup of $\sym{X}$; that is, it is a subset of $\sym{X}$ that contains the identity and is closed under composition and taking inverses.
\end{definition}

• Permutation group

definition needsreview rjosh