TITLE: What is the standard notation for group action
QUESTION [20 upvotes]: Please let me know what is the standard notation for group action.

I saw the following three notations for group action. 
(All the images obtained as G\acts X for different deinitions of \acts.) 
(1)  
I saw this one most, but only in handwriting and I like it. But I did not find a better way to write it in LaTeX.
\usepackage{mathabx,epsfig}
\def\acts{\mathrel{\reflectbox{$\righttoleftarrow$}}}

(2)  
It is almost as good as 1, but in handwriting this arrow can be taken as $G$.
\usepackage{mathabx}
\def\acts{\lefttorightarrow}

(3)  
I saw this one in print, I guess it is used since there is no better symbol in "amssymb".
\usepackage{amssymb} 
\def\acts{\curvearrowright}

REPLY [6 votes]: As this was the first hit on google for "latex action arrow", but didn't contain what I wanted, let me post what I figured out. But to address other people's issues with the original question: while I agree that in a sentence one should simply say "Let $G$ act on $X$...", I was interested in drawing a (what some people just generically call "commutative") diagram in order to visually display the relationships between several objects (as you do).
Anyway, there is a symbol $\circlearrowright$, which is almost what I wanted. If you do this:

\usepackage{graphicx}
  G\ \rotatebox[origin=c]{-90}{\$\circlearrowright\$}\ X

you will get an arrow whose beginning and end are right next to the X.