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\begin{document}

\title{Mini-HW 1\\Math 312, Spring 2023}
\author{Your name}

\maketitle


\begin{enumerate}
\item[1.1.1]  Complete the multiplication table for $D_8$ below.  (Use $\&$ symbol to separate entries in the table.)
\[\begin{array}{c|cccccccc}
&R_0 & R_{90} & R_{180} & R_{270} & H & V & D & D'\\
\hline
R_0 & R_0\\
R_{90} & R_{90} & R_{180} & & & D' & & H\\
R_{180} & R_{180} & R_{270} & & & V\\
R_{270}\\
H & & D\\
V\\
D\\
D'

\end{array}
\]
\item[1.1.5]
\begin{enumerate}
\item Find the center of $D_8.$  Type your answer here.
\item Find $\CC_{D_8}(R_{90})$ and $\CC_{D_8}(H)$.  Type your answer here.
\end{enumerate}

\item[1.1.6]  Complete the multiplication table for $D_6$ below.  Fill in the table the same way you did in 1.1.1.
\[\begin{array}{c|cccccc}
&R_0 & R_{120} & R_{240} &V & D& D' \\
\hline
R_0 & R_0\\
R_{120} & R_{120} & R_{240} & \\
R_{240} & R_{240} & R_0 & \\
V\\
D\\
D'

\end{array}
\]

\end{enumerate}

\begin{thebibliography}{99}
\bibitem{reference name} If you used any written sources (including electronic) other than our text, list them here.

\bibitem{human sources}  List human sources here.

\bibitem{shahriar}  Algebra in Action: A Course on Groups, Rings, and Fields, American Mathematical Socitey, 2017.
\end{thebibliography}
\end{document}
