Created the Abstract Algebra theorems and definitions cheat sheet

part-2/chapters/chapter-2/elementary-properties-of-groups.tex

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+\section{Elementary Properties of Groups}
+
+\begin{theorem}[Uniqueness of the Identity]
+	In a group $G$, there is only one identity element.
+\end{theorem}
+
+\begin{theorem}[Cancellation]
+	In a group $G$, the right and left cancellation laws hold; that is, $ba = ca$ implies $b = c$, and $ab = ac$ implies $b = c$.
+\end{theorem}
+
+\begin{theorem}[Uniqueness of Inverses]
+	For each element $a$ in a group $G$, there is a unique element $b$ in $G$ such that $ab = ba = e$.
+\end{theorem}
+
+\begin{theorem}[Socks-Shoes Property]
+	For group elements $a$ and $b$, $(ab)^{-1} = b^{-1}a^{-1}$.
+\end{theorem}