[[Group theory MOC]]
# Wreath product

Suppose $G$ is a group, $\Gamma$ is a set, and $H$ is a group acting on $\Gamma$.
Then the **wreath product** is the [[semidirect product]] #m/def/group 
$$
\begin{align*}
G^\Gamma \rtimes  H
\end{align*}
$$
where the action of $H$ on $G^\Gamma$ is induced by that on $\Gamma$.


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