LaTeX template for your adopted group paper

\documentclass[11pt]{article}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ...
%\geometry{landscape}                % Activate for for rotated page geometry
\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}


\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{propn}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}


\def\defn{\medskip\noindent{\bf Definition. }}
\def\proof{{\it Proof. }}
\def\qed{\hfill$\blacksquare$}



\title{Scintillating Title}
\author{Me, Of Course}
%\date{}                                           % Activate to display a given date or no date

\begin{document}
\maketitle
%\section{}
%\subsection{}

The group $D_3$ is fascinating, and we all should know why.  In Figure~\ref{cayley}, we see a Cayley table for the group.


\begin{table}[htdp]
\begin{center}
\begin{tabular}{c | c c c }  % the c is for 'center'; you could use l (left) or r (right)
% the | makes a vertical line
    $\times$  & $1$  & $R$  & $R^2$     \\
\hline % makes a horizontal line
  1 & $1$  & $R$  & $R^2$  \\
  $R$ & $R$  & $R^2$  & $1$  \\
  $R^2$ & $R^2$  & $1$  & $R$  \\
\end{tabular}
\end{center}
\caption{Cayley table for my fascinating group}
\label{cayley}   % This allows me to refer back to the table by the right number, even if I add more tables.
\end{table}%

\begin{theorem}\label{cyclic}
The group $D_3$ is cyclic\footnote{If you have questions for me as you write your paper, doing so in a footnote is a perfectly fine way of asking me something!}.
\end{theorem}

\proof
Observe that $D_3 =<R>$.
\qed

\end{document}