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\noindent{\Large{\textsc{Modern Algebra \hfill Assignment 15.1  \\ Spring 2023 \hfill Due April 28}}}

\large

\vspace{1cm}


\begin{exercise}
Let $G$ be a group which acts on a set $S$.  For $s, t \in S$ define $s \sim t$ if and only if there is a $g \in G$ so that $t = gs$.  Prove that $\sim$ is an equivalence relation on $S$.
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\begin{exercise}
Lang, exercise II.8.1.
\end{exercise}

\begin{exercise}
Lang, exercise II.8.2.
\end{exercise}

\begin{exercise}
Lang, exercise II.8.4.
\end{exercise}


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