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The standard notation for the semidirect of a group G by a group H is $G \rtimes H$ or $G\ltimes H$ depending on whether H is acting on G or G is acting on H. However, occasionally, people write the semidirect product using a colon. I've been typesetting this as $G:H$ but I find this produces too much space on either side of the colon. I alternatively tried typesetting this as $G\text:H$ but then the spacing is too tight. The spacing in superscripts/subscripts seems to more what I have in mind. For instance $\Phi^{G:H}$ seems to produce better spacing.

Is there an alternative option for using a colon in a math environment? Or is it possible to introduce my own colon and control the spacing myself?

I know there is \colon but this only reduces the spacing on one side and is more appropriate for function definitions, such as $f\colon G \to H$.

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    By default, : is of type mathrel. This means that in text style and display style, 5mu of whitespace ("thickspace") is inserted on either side. In script style and scriptscript style, though, no whitespace is inserted -- that's what you're observing in $\Phi^{G:H}$. If you like this look, you should be OK with ${G{:}H}$ as well. (Encasing a math item in curly braces converts it to type math-ordinary; such "atoms" do not get surrounded by whitespace.) Commented Mar 24, 2017 at 13:57

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I take it there's no chance that readers of your document will become confused between three potential meanings of : (a) relational operator, (b) \colon (with asymmetric spacing), and (c) symbol for "semidirect of a group". (If there is such a chance, you better stick with \ltimes and/or \rtimes for "semidirect of a group", right?)

If there's no chance for such confusion, you may want to set up a custom macro called, say, \sd, as follows:

\newcommand\sd{\mkern1.5mu{:}\mkern1.5mu} % "semidirect"

1.5mu is half of a thin-space. If that's not tight enough for your taste, try replacing the two instances of 1.5mu with 1mu.

Here's a comparison of various possible spacing choices:

enter image description here

\documentclass{article} \usepackage{array} \newcommand\sd{\mkern1.5mu{:}\mkern1.5mu} % "semidirect" \begin{document} \begin{tabular}{>{$}l<{$} >{\ttfamily}l} G\mathrel{:}H & \textbackslash mathrel (5mu) (default)\\ G\mathbin{:}H & \textbackslash mathbin (4mu) \\ G\,{:}\,H & 3mu symmetric \\ G\colon H & \textbackslash colon, 0mu/3mu asymmetric) \\ G\sd H & 1.5mu symmetric, \textbackslash sd\\ G\mathord{:}H & \textbackslash mathord (0mu)\\ \end{tabular} \end{document}
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    This is exactly what I was looking for. Thanks for your help! Commented Mar 24, 2017 at 14:37
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    I'll just add this in case it's of interest to anyone else. If you want the spacing to change in superscripts/subscripts then one can replace \mkern1.5mu with \mathchoice{\mkern1.5mu}{\mkern1.5mu}{}{}. This will mean in superscripts and subscripts there will be no additional spacing, just as with the normal usage of the colon. Commented Mar 24, 2017 at 15:37

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