A bijection from a finite group to the cyclic group with a divisibility property on the element orders

Abstract

We show that any finite group $G$ there exists a bijction $f$ from $G$ onto $C_n$ such that $o(x)$ divides $o(f(x))$ for all $x\in G$. This confirm Problem 18.1 in [7].

arXiv comment14 pages, I added some corrections