# Looking for a non-usual symbol for semidirect product

What I want are the symbols used in the textbook Theory of group representations and applications of Asom O. Barut and Ryszard Raczka (2n ed.) for semidirect sum and semidirect product. I upload a photo.

I have been looking for in Unicode symbols and i don't find anything, so probably it is going to be diffcult.

Thanks.

Remark. This question have been marked as possible duplicate question. I don't agree with that. I've tried to use Detexify to find my symbol, but it didn't recognize it. Probably I should study The Comprehensive LaTeX Symbol List better, but that is another question. Any of the answers provided in How to look up a symbol or identify a math symbol or character? solves my problem.

You can build the symbols yourself.

\documentclass{article}
\usepackage{pict2e}

\makeatletter
\DeclareRobustCommand{\loplus}{\mathbin{\mathpalette\dog@lsemi{+}}}
\DeclareRobustCommand{\lotimes}{\mathbin{\mathpalette\dog@lsemi{\times}}}
\DeclareRobustCommand{\roplus}{\mathbin{\mathpalette\dog@rsemi{+}}}
\DeclareRobustCommand{\rotimes}{\mathbin{\mathpalette\dog@rsemi{\times}}}

\newcommand{\dog@rsemi}[2]{\dog@semi{#1}{#2}{-90,90}}
\newcommand{\dog@lsemi}[2]{\dog@semi{#1}{#2}{270,90}}
\newcommand{\dog@semi}[3]{%
\begingroup
\sbox\z@{$\m@th#1#2$}%
\setlength{\unitlength}{\dimexpr\ht\z@+\dp\z@\relax}%
\makebox[\wd\z@]{\raisebox{-\dp\z@}{%
\begin{picture}(1,1)
\linethickness{\variable@rule{#1}}
\roundcap
\put(0.5,0.5){\makebox(0,0){\raisebox{\dp\z@}{$\m@th#1#2$}}}
\put(0.5,0.5){\arc[#3]{0.5}}
\end{picture}%
}}%
\endgroup
}
\newcommand{\variable@rule}[1]{%
\fontdimen8
\ifx#1\displaystyle\textfont3\else
\ifx#1\textstyle\textfont3\else
\ifx#1\scriptstyle\scriptfont3\else
\scriptscriptfont3\relax
\fi\fi\fi
}
\makeatother

\begin{document}

$A\roplus B\rotimes C\loplus D \lotimes E$

$\scriptstyle \roplus\rotimes\loplus\lotimes$

\end{document}


However, note that the standard \oplus and \otimes are lighter than + and \times, so you may want to redefine also them in a similar way, using the full circle.

I have just found it. It is defined in stix package, as: \oplusrhrim and \otimesrhrim.

• Notice that many authors (ab)use the $\ltimes$ and $\rtimes$ symbols for that (mainly because issues with the interplay between stix and amsmath, see section 2.2 of the stix manual).
– user121799
Feb 16, 2018 at 19:50
• I thought \rtimes and \ltimes were the snatdard symbols. They aren't the usual? Feb 16, 2018 at 20:03
• What do you mean by "standard"? They come with a vertical bar on the either left- or right-hand side, and thus resemble your symbols, and they are widely used in the literature (even though the one you found look more like the original ones).
– user121799
Feb 16, 2018 at 20:15
• What I wanted to say is that I thought the ''canonical'' to denote the semidirect product was the \rtimes, for example in Wikipedia's article. And that until Barut and Raczka's book, I'd not seen these symbols. But I agree with you. From my point of view, stix's symbols seems more natural or ''correct''. Feb 16, 2018 at 21:08