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MATH 440: Chapter 3 Write-Up Problems\vspace{1em}

Name:\vspace{1em}
\begin{enumerate}

\item Prove or disprove: Every group of order 6 is abelian.
%162.J9.32.5

\item Prove or disprove: If $H$ and $K$ are subgroups of a group $G$, then $H \cup K$ is a subgroup of $G$.
%189.J3.76.21

\item Fix an element $h \in G$ a group and consider the set $$hG = \{hg \mid g \in G\}.$$ Prove or disprove: As sets, $hG=G$.
%266.P24.151.7

\end{enumerate}

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