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% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}  \DeclareMathOperator{\aut}{Aut} 
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\begin{definition}
Let $X$ be a set possibly equipped with additional structure, e.g. $X$ is the vertex set of a graph or $X$ is the underlying set of a group. The permutations of $X$ ``preserving the additional structure'' is called the \textdef{automorphism group} of the structure, denoted $\aut(X)$.
\end{definition}