I'd like to place p evenly-spaced nodes around a circle.
I want to draw the following picture with using document class [report].

Edit: What I have done so far,
\documentclass[a4paper,leqno,11pt]{amsart}
\usepackage{amsfonts,amssymb,verbatim,amsmath,amsthm,latexsym,textcomp,amscd}
\usepackage{latexsym,amsfonts,amssymb,epsfig,verbatim}
\usepackage{amsmath,amsthm,amssymb,latexsym,graphics,textcomp}
%\usepackage[all,2cell,dvips]{xy}
\usepackage{graphicx}
\usepackage{color}
\usepackage{url}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\def \n {5}
\def \radius {1.5cm}
\def \margin {3}
\foreach \s in {1,...,\n} {%
\node [anchor=center] at ({360/\n * (\s-1)}:\radius+ 1){$g^{\s}$};
\filldraw[black] ({360/\n * (\s-1)}:\radius) circle (1pt) ;
\node [anchor=center] at ({360/\n * (\s-1)}:\radius+0.3cm ){$g^{\s}$};
\draw[>=latex] ({360/\n * (\s-1)+ \margin}:\radius)
arc({360/\n * (\s-1)+\margin}:{360/\n * (\s)-\margin}:\radius);
}
\end{tikzpicture}
\end{document}

