\documentclass[minion]{homework}

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\def\ip<#1,#2>{\left<#1,#2\right>}
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\doclabel{Math F490: Homework 6}
\docdate{Due: February 27, 2019}

\begin{document}
\begin{problems}
\problem 3.5.1
\problem 3.5.2
\problem 3.5.3

\problem  Suppose $H$ is a torus in $G$.  Moreover,
suppose that $H$ has the property that if $g\in G$
commutes with all elements of $H$, then $g\in H$.
Conclude that $H$ is a maximal torus.

You should be aware that the proof on pages 64--66 showed
that the subgroups are maximal tori by exactly 
establishing the above fact.

\problem Show that the converse of the previous problem is false.
That is, find a group $G$ containing a maximal torus $H$, but
also such that there is an element of $G$ not contained in $H$
that commutes with all elements of $H$.

\problem 3.6.3 Hint: You've already done the work.

\problem 3.6.4

\end{problems}

\end{document}
