Created the Abstract Algebra theorems and definitions cheat sheet

part-5/chapters/chapter-29/burnsides-theorem.tex

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+\section{Burnside's Theorem}
+
+\begin{definition}[Elements Fixed by $\mathbf{\phi}$]
+	For any group $G$ of permutations on a set $S$ and any $\phi$ in $G$, we let $\fix(\phi) = \{i \in S\ \vert\ \phi(i)=i\}$. This set is called the \textit{elements fixed by $\phi$} (or more simply, "fix of $\phi$").
+\end{definition}
+
+\begin{theorem}[Burnside's Theorem]
+	If $G$ is a finite group of permutations on a set $S$, then the number of orbits of elements of $S$ under $G$ is
+	\[ \frac{1}{\abs{G}}\sum_{\phi \in G}\abs{\fix(\phi)} \]
+\end{theorem}