Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{The Frieze Groups}
+
+\begin{remark}
+	In this chapter, we discuss an interesting collection of infinite symmetry groups that arise from periodic designs in a plane. There are two types of such groups. The \textit{discrete frieze groups} are the plane symmetry groups of patterns whose subgroups of translations are isomorphic to $\Z$. These kinds of designs are the ones used for decorative strips and for patterns on jewelry. In mathematics, familiar examples include the graphs of $y=\sin(x)$, $y=\tan(x)$, $y=\abs{\sin(x)}$, and $\abs{y} = \sin(x)$. After we analyze the discrete frieze groups, we examine the discrete symmetry groups of plane patterns whose subgroups of translations are isomorphic to $\Z \oplus \Z$.
+\end{remark}