While reading some (relatively old) papers on group-theory I encountered the following notations whose meanings I cannot understand:


If $W= G \wr H$ is the (unrestricted) wreath product of $G$ and $H$, $f$ an element of the basis $G^H$ and $h$ an element of $H$, what do 
$f^H$ and $h^W$ mean? 


Just for the sake of completeness: the action of $h \in H$ on $f \in G^H$ is denoted by $f^h$



Notation on wreath product
If the action is written in exponential notation, then $f^H = \{f^h \mid h\in H\}$. Similarly $W$ acts on itself by conjugation which is also frequently written in exponential notation so that $h^W = \{w^{-1}hw \mid w\in W\}$. It is maybe better not to use $G^H$ for the set of all set maps $H\to G$ in this situation and use something like $Map(H,G)$ instead.


