Semidirect product (⋉,⋊,⋋,⋌) in LaTeX

In mathematics, there are four types of Semidirect product:

• Left Normal Factor Semidirect Product (⋉)
• Right Normal Factor Semidirect Product (⋊)
• Left Semidirect Product (⋋)
• Right Semidirect Product (⋌)

In this tutorial, I will show you how to get all of these Semidirect product symbols in LaTeX.

There is no default command to get these symbols, so you have to use packages. And multiple packages provide commands to get these symbols in LaTeX.

Semidirect product symbols (⋉,⋊,⋋,⋌) with amssymb package

The amssymb package provides some commands to get these Semidirect product symbols in LaTeX.

• Left Normal Factor Semidirect Product (⋉): \ltimes
• Right Normal Factor Semidirect Product (⋊): \rtimes
• Left Semidirect Product (⋋): \lightthreetimes
• Right Semidirect Product (⋌): \rightthreetimes

Take a look.

\documentclass{article}
\usepackage{amssymb}
\begin{document}

  $$ A \ltimes B $$
  $$ A \rtimes B $$
  $$ A \leftthreetimes B $$
  $$ A \rightthreetimes B $$
  
\end{document}

Output:

Semidirect product symbols with stix package

You can also use the stix package to get these symbols in LaTeX. All the commands will be the same.

\documentclass{article}
\usepackage{stix}
\begin{document}

  $$ A \ltimes B $$
  $$ A \rtimes B $$
  $$ A \leftthreetimes B $$
  $$ A \rightthreetimes B $$
  
\end{document}

Output:

Semidirect product symbols with MnSymbol package

To get a slightly different style of the Semidirect product symbols you can use the MnSymbol package.

\documentclass{article}
\usepackage{MnSymbol}
\begin{document}

  $$ A \ltimes B $$
  $$ A \rtimes B $$
  $$ A \leftthreetimes B $$
  $$ A \rightthreetimes B $$
  
\end{document}

Output:

Semidirect product symbols with fdsymbol package

The fdsymbol package also provides those commands to get the Semidirect product symbols in LaTeX.

\documentclass{article}
\usepackage{fdsymbol}
\begin{document}

  $$ A \ltimes B $$
  $$ A \rtimes B $$
  $$ A \leftthreetimes B $$
  $$ A \rightthreetimes B $$
  
\end{document}

Output: