A remark on the number of automorphisms of finite abelian groups

Abstract

Let $A{b}_0$ be the class of finite abelian groups and consider the function $f:A{b}_0⟶(0,\infty )$ given by $f(G)=\frac{|\mathrm{Aut}(G)|}{|G|}$\,, where $\mathrm{Aut}(G)$ is the automorphism group of a finite abelian group $G$. In this short note, we prove that the image of $f$ is a dense set in $[0,\infty )$.

Accepted for publication in Elem. Math