Power map permutations and symmetric differences in finite groups

Márton Hablicsek, Guillermo Mantilla-Soler

Let $G$ be a finite group. For all $a\in \mathbb{Z}$, such that $(a,|G|)=1$, the function ${\rho }_a:G\to G$ sending $g$ to $g^a$ defines a permutation of the elements of $G$. Motivated by a…