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For a finite group $G$, multiplying every element on the right by a fixed element $h \in G$ merely permutes the elements of $G$. The set $\{gh \mid g \in G\}$ is exactly $G$.

Conditions: $G$ is a finite group.; $h$ is a fixed element in $G$.; $f$ is any function defined on $G$.

For a finite group $G$, multiplying every element on the right by a fixed element $h \in G$ merely permutes the elements of $G$. The set $\{gh \mid g \in G\}$ is exactly $G$.

Conditions: $G$ is a finite group.; $h$ is a fixed element in $G$.; $f$ is any function defined on $G$.