a commutative diagram compatible with group actions

I'm trying to draw the following commutative diagram using xymatrix:

\documentclass{article}
\usepackage[all]{xy}

\begin{document}

$\xymatrix{A \ar[rr] & & B \\ & C \ar[ul] \ar[ur] & }$

\end{document}


How can I draw symbols of group action?

• Welcome to TeX.SX! Please make your code compilable (if possible), or at least complete it with \documentclass{...}, the required \usepackage's, \begin{document}, and \end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – Adam Liter Apr 16 '15 at 3:29
• Sorry...I edited my question. – KOTO Apr 16 '15 at 4:08
• Is there any particular style that you would like for your arrows (e.g. their orientation, their location relative to A, B, C, etc.)? – Niel de Beaudrap Apr 16 '15 at 18:09
• Since you have some responses below that seem to answer your question, please consider marking one of them as ‘Accepted’ by clicking on the tickmark below their vote count (see How do you accept an answer?). This shows which answer helped you most, and it assigns reputation points to the author of the answer (and to you!). It's part of this site's idea to identify good questions and answers through upvotes and acceptance of answers. – LaRiFaRi May 19 '15 at 8:05

Or like this:

% arara: pdflatex

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}
$\begin{tikzcd} A \arrow{rr}\arrow[loop left, "G_1"] & & B \arrow[loop right, "G_2"] \\ & C \arrow{ul} \arrow{ur} \arrow[loop below, "G_3"] & \end{tikzcd}$
\end{document}


Here's a solution using TiKZ instead of xypics. The arrows are drawn as circular arcs with modifiable parameters; the location and style for the labels of the group actions can also be varied.

Some particular remarks on the code:

• The group actions are denoted by nearly complete circles (omitting 45° of the turn), whose orientations can be modified by changing the starting and ending angles.

• The end tips of each arrow are elongated, in order to better match the appearance of the orientation of the arrow-head with the angle at which the arc ends.

Source code

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[-stealth]
% Position nodes symmetrically about a central point
\node (A) at ({cos(150)},{sin(150)}) {$A$};
\node (B) at ({cos(30)},{sin(30)}) {$B$};
\node (C) at ({cos(270)},{sin(270)}) {$C$};

% Draw arrows between nodes
\draw (A) to (B); \draw (C) to (A); \draw (C) to (B);

% Define co-ordinates for the arrows of the group actions
\coordinate (G1') at ($(A.west) + (-0.5em,0)$);
\coordinate (G2') at ($(B.east) + (0.5em,0)$);
\coordinate (G3') at ($(C.south west) + (0.5em,-2ex)$);

% Draw circular arcs of 1ex radius for the group actions
% (tips are slightly lengthened to optimise orientation of arrow head)
\draw [->, shorten >=-1.5pt] (G1') arc (245:-70:1ex);
\draw [->, shorten >=-1.5pt] (G2') arc (-65:250:1ex);
\draw [->, shorten >=-1.5pt] (G3') arc (315:0:1ex);

% Draw labels for the group actions, smaller than the main nodes
\node (G1) at ($(G1') + (-1em,0)$) {\footnotesize $G_1$};
\node (G2) at ($(G2') + (1em,0)$) {\footnotesize $G_2$};
\node (G3) at ($(G3') + (0,-2ex)$) {\footnotesize $G_3$};
\end{tikzpicture}
\end{document}


Result

Something like this? (With help of this documentation, p. 4, since I'm not very proficient in xy-pic.)

\documentclass{article}
\usepackage[all,cmtip]{xy}
\begin{document}
$\xymatrix{ A \ar@(dl,ul)[]^{G_1} \ar[rr] & & B \ar@(dr,ur)[]_{G_2} \\ & C \ar@(dl,dr)[]_{G_3}\ar[ul] \ar[ur] & }$
\end{document}


Edit: following LaRiFari's suggestion, now the cmtip option is used.The arrow heads are much better looking!

• May I recommend loading \usepackage[all,cmtip]{xy}? Personal taste, but see the difference! – LaRiFaRi Apr 16 '15 at 7:54
• @LaRiFaRi Thanks for the… tip :-) Suggestion adopted! – Franck Pastor Apr 16 '15 at 7:59