\documentclass{amsart}
\usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package
                                % Using postscript driver for smoother curves
\usepackage{color}              % For invisible frame
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix@=6pt{
&\{\pm 1\}
  \ar@{^(->}@/_1pc/[ddl]_{a^n}
  \ar@{_(->}@/^1pc/[ddr]^{a^n}
\\ \\
   C_{2n}               \ar@{->>}[dd] \ar@{^(->}[rr]
 &&\operatorname{Dic}_n \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]
\\
 &&                                                             &&\{\pm 1\}
\\
   C_n                  \ar@{^(->}[rr]
 &&\operatorname{Dih}_n \ar@{->>}@/_1pc/[rru]
}

$$}}} % end math, end frame
\end{document}