Created the Abstract Algebra theorems and definitions cheat sheet

part-2/chapters/chapter-9/applications-of-factor-groups.tex

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+\section{Applications of Factor Groups}
+
+\begin{theorem}[$\mathbf{G/Z}$ Theorem]
+	Let $G$ be a group and let $Z(G)$ be the center of $G$. If $G/Z(G)$ is cyclic, then $G$ is Abelian.
+\end{theorem}
+
+\begin{theorem}[$\mathbf{G/Z(G) \approx \text{Inn}(G)}$]
+	For any group $G$, $G/Z(G)$ is isomorphic to Inn$(G)$.
+\end{theorem}
+
+\begin{theorem}[Cauchy's Theorem for Abelian Groups]
+	Let $G$ be a finite Abelian group and let $p$ be a prime that divides the order of $G$. Then $G$ has an element of order $p$.
+\end{theorem}