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\noindent{\Large{\textsc{Modern Algebra \hfill Assignment 6.3  \\ Spring 2019 \hfill Due February 27}}}

\large

\vspace{1cm}

\begin{exercise}
Compute $[\R^{\times} : \R^+]$.
\end{exercise}

\begin{exercise}
Let $G$ be a group of order $pqr$, where $p$, $q$ and $r$ are distinct primes.  If $H, K < G$ satisfy $|H|=qp$ and $|K|=qr$, prove that $|H \cap K| = q$. [{\em Suggestion:}  Begin by observing that $K$ has more elements than $H$ has (left) cosets.]
\end{exercise}

\begin{exercise}
Lang, II.4.4
\end{exercise}

\begin{exercise}
Lang, II.4.28
\end{exercise}

\begin{exercise}
Lang, II.4.29
\end{exercise}

\end{document}
