File:PSL-PGL.svg

\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{
   \mathrm{SZ}(V)         \ar@{^(->}[r]                      \ar@{^(->}[d]
 & \mathrm{Z}(V)\cong F^* \ar@{->>}[r]^(.6){\det \cong z^n}  \ar@{^(->}[d]
 & (F^*)^n                                                   \ar@{^(->}[d] \\
   \mathrm{SL}(V)         \ar@{^(->}[r]                  \ar@{->>}[d]
 & \mathrm{GL}(V)         \ar@{->>}[r]^{\det}            \ar@{->>}[d]
 & F^*                                                   \ar@{->>}[d] \\
   \mathrm{PSL}(V)        \ar@{^(->}[r]
 & \mathrm{PGL}(V)        \ar@{->>}[r]
 & F^*/(F^*)^n
}
 
$$}}} % end math, end frame
\end{document}