Extendable birational transformations belonging to Galois points

We study birational transformations belonging to Galois points. Let P be a Galois point for a plane curve C and GP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_P$$\end{document} be a Galois group at P. Then an element of GP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_P$$\end{document} induces a birational transformation of C. In general, it is difficult to determine when this birational transformations can be extended to a Cremona (or projective) transformation. In this note, we shall prove that if the Galois group is isomorphic to the cyclic group of order three, then any element of the Galois group has an expression as a de Jonqui & egrave;res transformation. In particular, they can be extended to Cremona transformations.