Created the Abstract Algebra theorems and definitions cheat sheet

part-5/chapters/chapter-27/chapter-27.tex

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+\chapter{Symmetry Groups}
+\subimport{./}{isometries.tex}
+\subimport{./}{classification-of-finite-plane-symmetry-gruops.tex}
+\subimport{./}{classification-of-finite-groups-of-rotations-in-R3.tex}

part-5/chapters/chapter-27/classification-of-finite-groups-of-rotations-in-R3.tex

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+\section{Classification of Finite Groups of Rotations in $\mathbf{\R^3}$}
+
+\begin{theorem}[Finite Groups of Rotations in $\mathbf{\R^3}$]
+	Up to isomorphism, the finite groups of rotations in $\R^3$ are $\Z_n$, $D_n$, $A_r$, $S_4$, and $A_5$.
+\end{theorem}

part-5/chapters/chapter-27/classification-of-finite-plane-symmetry-gruops.tex

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+\section{Classification of Finite Plane Symmetry Groups}
+
+\begin{theorem}[Finite Symmetry Groups in the Plane]
+	The only finite plane symmetry groups are $\Z_n$ and $D_n$.
+\end{theorem}

part-5/chapters/chapter-27/isometries.tex

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+\section{Isometries}
+
+\begin{remark}
+	It is convenient to begin our discussion with the definition of an isometry (from the Greek \textit{isometros}, meaning "equal measure") in $\R^n$.
+\end{remark}
+
+\begin{definition}[Isometry]
+	An \textit{isometry} of $n$-dimensional space $\R^n$ is a function from $\R^n$ onto $\R^n$ that preserves distance.
+\end{definition}
+
+\begin{definition}[Symmetry Group of a Figure in $\mathbf{\R^n}$]
+	Let $F$ be a set of points in $\R^n$. the \textit{symmetry group of $F$} in $\R^n$ is the set of all isometries of $\R^n$ that carry $F$ onto itself. The group operation is function composition.
+\end{definition}