Created the Abstract Algebra theorems and definitions cheat sheet

part-5/chapters/chapter-24/the-class-equation.tex

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+\section{The Class Equation}
+
+\begin{corollary}[Class Equation]
+	For any finite group $G$,
+	\[ \abs{G} = \sum \abs{G:C(a)} \]
+	where the sum runs over one element of $a$ from each conjugacy class of $G$.
+\end{corollary}
+
+\begin{theorem}[$\mathbf{p}$-Groups Have Nontrivial Centers]
+	Let $G$ be a nontrivial finite group whose order is a power of a prime $p$. Then $\Z(G)$ has more than one element.
+\end{theorem}
+
+\begin{corollary}[Groups of Order $\mathbf{p^2}$ Are Abelian]
+	If $\abs{G}=p^2$, where $p$ is prime, then $G$ is Abelian.
+\end{corollary}